Tire transient response data calculating method, data processing method, tire designing method, vehicle motion predicting method, and tire cornering characteristic evaluation method and evaluation device therefor

ABSTRACT

Tire transient response data during cornering with a slip angle is calculated based on a tire dynamic model. A deformation response of a tread part in the tire dynamic is set as a first-order-lag response. The value of the transient response parameter is initialized, to define the first-order-lag response. The time-series data of the transient response of the slip angle between the tread part and a road surface in the tire dynamic model is obtained by computing a convolution integral of the defined response function of the first-order-lag response with a time gradient of the time-series data of the slip angle. A value of a lateral force is calculated by using the tire dynamic model based on the obtained time-series data of the transient response of the slip angle. Accordingly, the transient response data is calculated, and a value of the transient response parameter is obtained.

BACKGROUND OF THE INVENTION

The present invention relates to a transient response data calculating method for calculating transient response data of a tire during cornering or braking/driving based on a tire dynamic model that is built from at least one dynamic element parameter, a data processing method for calculating the value of a transient response parameter of a response function of the tire dynamic model that determines the behavior of transient response, and a tire designing method and a vehicle motion predicting method which use the transient response calculating method. The present invention also relates to a tire cornering characteristic evaluating method and device for quantitatively evaluating a transient response characteristic of a tire lateral force which is generated in a tire rolling at a slip angle.

The recent increase in engine power has brought about performance enhancement of passenger vehicle tires by a higher aspect ratio with the intent of improving a vehicle's maximum cornering capability and responsiveness, and traction performance as well. Despite the enhancement, it cannot positively be said that the steering stability in infinitesimal steering at high speed has been improved and, with the advance of express ways, development of a tire that is excellent in steering stability in infinitesimal steering at high speed is a very important matter. A great contributing factor to the steering stability performance of a tire fit to a vehicle is tire cornering characteristic, which is a characteristic related to a response characteristic when a vehicle is steered quickly.

A cornering characteristic of a tire is expressed by a response in the form of a tire lateral force, a cornering force, a self-aligning torque, or the like to an input to the tire such as a load, a slip angle, a camber angle, or a slip ratio when the tire is steered quickly. Lately, the demand for development of a high performance tire that exhibits good steering stability even in infinitesimal steering at high speed has created a need for a method and a device that are capable of evaluating, quantitatively, with precision, a cornering characteristic of a tire alone.

Moreover, since a tire is the only thing between a vehicle and the road surface that transfers a force from the road surface to the vehicle, tires play an important role in today's automobile industry which seeks advanced vehicle control for safe vehicle driving and avoidance of danger. Analyzing a cornering characteristic of a tire is therefore necessary.

“Actual ride feeling test” in which a test tire is fit to a vehicle and an evaluator steers the vehicle to obtain information about steering stability felt by the evaluator is one of conventional testing methods for evaluating steering stability. The actual ride feeling test has an advantage in that information is obtained about steering stability in actual steering, but the evaluation based on senses of an evaluator is not quantitative.

As a tire cornering characteristic analyzing method, there is known a method described in JP 2005-88832 A. This publication discusses a calculation in which a cornering characteristic of a tire in a steady state when a slip angle is given as time-series data is calculated based on a tire dynamic model that is built from multiple tire dynamic element parameters. The publication says that in this way, a tire can be designed efficiently.

With the above-mentioned tire dynamic model, a cornering characteristic in a steady state can be obtained by giving a slip angle, but it is not possible to reproduce a transient response during cornering which changes with a slip angle given to the tire dynamic model in time series. In emergency quick steering for avoiding a danger, in particular, a lateral force and a self-aligning torque that the quick steering generates in a tire exhibit transient characteristics different from those in a steady state, and it is therefore meaningless to analyze vehicle motion from a cornering characteristic in a steady state.

Furthermore, today's vehicles are braked usually with the use of an anti-lock break system (ABS), which controls the slip ratio on a few Hz basis so that the maximum braking power is always obtained upon braking. The generated braking power is therefore based on a characteristic in a transient state which differs from that in a steady state. Accordingly, it is meaningless to analyze the motion of a vehicle that has an ABS from a longitudinal force in a steady state that is calculated with the use of the above-mentioned tire dynamic model.

Evaluation of a tire dynamic characteristic with the use of an indoor cornering testing machine is also practiced in order to evaluate a cornering characteristic of a tire alone quantitatively with precision. Iida, “Influence of Tire Dynamic Characteristics on Vehicle Motion Performance”, Automotive Engineering, 1984, no. 3, vol. 38, p. 320 is given as an example. In an example of the conventional way of evaluating a cornering dynamic characteristic for evaluating a tire dynamic characteristic with the use of an indoor cornering testing machine, a tire is rolled on a contact patch at a constant rolling speed, and slip angle inputs are given to the tire at different frequencies to obtain a response characteristic in the form of a lateral force, a cornering force, a self-aligning torque, or the like with respect to a distance frequency (a distance frequency characteristic). The distance frequency characteristic is determined by the ratio of an angular speed ω of a slip angle input with respect to a tire rolling speed.

SUMMARY OF THE INVENTION

It is a known fact that a distance frequency response characteristic of a tire lateral force with respect to a given slip angle (will be referred to as distance frequency characteristic) does not match the result of the aforementioned actual ride feeling test well. This is because a distance frequency characteristic changes in accordance with the rolling speed of a tire. One of possible reasons that a distance frequency characteristic changes in accordance with the rolling speed of a tire is that the temperature of a rolling tire changes in accordance with the rolling speed of the tire, which more or less changes the cornering characteristic of the tire itself. Also, indoor cornering testing machines measure output information such as a tire lateral force by repeatedly applying to a tire a slip angle that changes continuously in a sine wave fashion in time series. A tire rolling at a slip angle reaches an excessively high temperature and degrades faster. Moreover, successive inputs of slip angles are far different from time-series slip angles generated in a tire during actual driving of a vehicle. It stands to reason that a response such as a tire lateral force to a slip angle that changes continuously in a sine wave fashion in time series will not reflect the result of an actual ride feeling test. In short, a tire lateral force obtained as a response to a slip angle that changes continuously in a sine wave fashion does not match the result of an actual ride feeling test. Furthermore, it is unclear how lateral force data obtained as a tire response should be processed in order to make the lateral force data consistent with the result of an actual ride feeling test.

Also available nowadays is evaluation of various conceptual tires, which are merely under consideration and not manufactured even experimentally, through simulation with the use of a finite element method and finite element models reproducing various conceptual tires. However, this has a problem in that a cornering characteristic of a conceptual tire cannot be evaluated with precision in a manner that makes it consistent with the result of an actual ride feeling test since it is unclear how tire lateral force data obtained as a response to an input slip angle should be processed as mentioned above.

The present invention has been made to solve the above-mentioned problems, and an object of the present invention is therefore to provide a method of calculating transient response data of a tire during cornering and braking/driving to calculate a transient response of the tire with the use of a tire dynamic model, a data processing method for determining the value of a parameter that determines the transient response and is used in the tire model, and a tire designing method and a vehicle motion predicting method which use the transient response data calculating method, as well as a tire cornering characteristic evaluating method and evaluating device which are capable of accurately evaluating and predicting a tire cornering characteristic equivalent to that of when a vehicle is actually steered for a test tire or for a conceptual tire which is under consideration but yet to be manufactured experimentally.

The present invention provides a tire transient response data calculating method, for calculating tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, comprising the steps of:

(1) acquiring a value of at least one tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; (2) calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip angle provided to the tire dynamic model, the first-order-lag response specifying a deformation response of the tread part during cornering; and (3) calculating, as transient response data during cornering, output data of at least one of a lateral force and self-aligning torque by using the tire dynamic model based on the calculated time-series data of the transient response of the slip angle.

It the invention, it is preferable that the time-series data of the slip angle provided to the tire dynamic model is modified by torsional deformation of the tire dynamic model which is caused by a self-aligning torque during cornering, and the modified time-series data is used for calculating the time-series data of the transient response of the slip angle. The torsional deformation of the tire which is generated by the self-aligning torque is preferably represented by dividing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of previous time-series data of the self-aligning torque, by a value of a stiffness contained in the tire dynamic model, the first-order-lag response specifying a deformation response of a side part during cornering.

The output data calculated using the tire dynamic model may comprise data of the lateral force corrected by lateral bending deformation of a belt part generated by the lateral force. The lateral bending deformation of the belt part generated by the lateral force is preferably represented by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of previous time-series data of the generated lateral force, the first-order-lag response specifying a deformation response of the belt part during cornering.

The invention also provides a tire transient response data calculating method, for calculating tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model, comprising the steps of:

(1) previously acquiring values of at least one of a lateral force and a self-aligning torque in a steady state from actual measurement of a tire by providing a tire with the time-series data of the slip angle varying across at least a range between 0 degrees and a predetermined angle as the slip angle in the steady state; (2) calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip angle provided to the tire, the first-order-lag response specifying a deformation response of the tread part during cornering; and (3) acquiring, as transient response data during cornering, the time-series data of at least one of the lateral force and self-aligning torque in a transient state by obtaining a value of at least one of the lateral force and self-aligning torque in the steady state corresponding to each value of the calculated time-series data of the transient response of the slip angle.

The invention also provides a data processing method, in which a deformation response of a tread part which specifies a transient response during cornering in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of:

(1) previously acquiring measurement data of the transient response of at least one of a lateral force and self-aligning force during cornering of a tire by providing the tire with the time-series data of a slip angle as a measurement condition; (2) setting a value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable, thereby making the tire dynamic model operable; (3) performing simulating calculation including:

(a) obtaining the time-series data of a transient response of the slip angle between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the defined response function of the first-order-lag response with a time gradient of the time-series data of the slip angle provided to the tire as the measurement condition;

(b) calculating, as the time-series data of at least one of the lateral force and the self-aligning torque in a transient state during cornering, values of at least one of the lateral force and the self-aligning torque by using the tire dynamic model based on the obtained time-series data of the transient response of the slip angle; and

(3) obtaining a sum of square residuals between the calculated time-series data of at least one of the lateral force and self-aligning torque and the measurement data of the tire, repeating the simulating calculation while correcting the set value of the transient response parameter until the sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.

The invention provides a data processing method, in which a deformation response of a tread part which specifies a transient response during cornering in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of:

(1) previously acquiring measurement data of the transient response of at least one of a lateral force and a self-aligning torque during cornering of a tire by providing the tire with the time-series data of a slip angle, which varies across at least a range between 0 degrees and a predetermined angle while the slip angle reciprocates, as a measurement condition; (2) setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; (3) performing regression calculation including:

(a) obtaining the time-series data of a transient response of the slip angle between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the response function of the first-order-lag response with a time gradient of the time-series data of the slip angle provided to the tire as the measurement condition;

(b) subjecting a characteristic curve, which represents a values of at least one of the lateral force and the self-aligning torque with respect to values of the obtained time-series data of the transient response of the slip angle, to least square regression into a single smooth curve by using a curve function; and

(c) obtaining a sum of square residuals between the least square regression curve obtained by the least square regression and the characteristic curve; and

(4) repeating the regression calculation while correcting the set value of the transient response parameter until the calculated sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.

The invention provides a tire transient response data calculating method, for calculating tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, comprising the steps of:

(1) acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; (2) calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip ratio provided to the tire dynamic model, the first-order-lag response specifying a deformation response of the tread part during braking/driving,; and (3) calculating, as transient response data during braking/driving, output data of a longitudinal force by using the tire dynamic model based on the time-series data of the transient response of the slip ratio.

The invention provides a tire transient response data calculating method, for calculating tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model, comprising the steps of:

(1) previously acquiring values of a longitudinal force in a steady state from actual measurement of the tire when the time-series data of the slip ratio varying across at least a range between 0 degrees and a predetermined slip ratio is provided as the slip ratio in the steady state; (2) calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip ratio, the first-order-lag response specifying a deformation response of the tread part during braking/driving; and (3) acquiring, as transient response data during braking/driving, the time-series data of the longitudinal force in a transient state by obtaining a value of the longitudinal force in the steady state corresponding to each value of the calculated time-series data of the transient response of the slip ratio.

The invention also provides a data processing method, in which a deformation response of a tread part which specifies a transient response during braking/driving of a tire in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of:

(1) previously acquiring measurement data of the transient response of a longitudinal force during braking/driving of a tire by providing the tire with the time-series data of a slip ratio, which varies across at least a range between 0 degrees and a predetermined slip ratio while the slip ratio reciprocates, as a measurement condition; (2) setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; (3) performing regression calculation including:

(a) obtaining the time-series data of a transient response of the slip ratio between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the response function of the first-order-lag response with a time gradient of the time-series data of the slip ratio provided to the tire as the measurement condition;

(b) subjecting a characteristic curve, which represents values of the longitudinal force with respect to values of the obtained time-series data of the transient response of the slip ratio, to least square regression into a single smooth curve by using a curve function; and

(c) obtaining a sum of square residuals between the least square regression curve obtained by the least square regression and the characteristic curve; and

(4) repeating the regression calculation while correcting the set value of the transient response parameter until the calculated sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.

The invention provides a data processing method, in which a deformation response of a tread part which specifies a transient response during braking/driving in a tire dynamic model constituted by using at least one tire dynamic element parameter is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of:

(1) previously acquiring measurement data of the transient response of a longitudinal force during braking/driving of a tire by providing the tire with the time-series data of a slip ratio in a longitudinal direction of the tire as a measurement condition; (2) setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; (3) performing simulating calculation including:

(a) obtaining the time-series data of a transient response of the slip ratio between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the defined response function of the first-order-lag response with a time gradient of the time-series data of the slip ratio provided to the tire as the measurement condition;

(b) calculating a longitudinal force by using the tire dynamic model based on a value of the obtained time-series data of the transient response of the slip ratio, to obtain the time-series data of the longitudinal force in a transient state during braking/driving; and

(c) calculating a sum of square residuals of the calculated time-series data of the longitudinal force and the measurement data of the tire, repeating the simulating calculation while correcting the set value of the transient response parameter until the sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.

Above these inventions can be adapted a tire designing method or a vehicle motion predicting method.

For example, the tire transient response data calculated by the tire transient response data calculating method is repeatedly calculating and outputting while correcting the value of the tire dynamic element parameter or a value of a transient response parameter that defines the first-order-lag response by adjusting a tire component member that defines the tire dynamic element parameter or the first-order-lag response until the output transient response data satisfies a preset target condition; and the tire component member is determined as a target tire component member when the output data satisfies the target condition.

The transient response data calculated by the tire transient response data calculating method is used for predicting a vehicle motion based on a vehicle model in which the transient response data is provided to an axle portion of the vehicle model.

The invention also provides a method of evaluating a cornering characteristic of a tire when a slip angle is provided as time-series data, comprising the steps of:

(1) acquiring time-series lateral force data with respect to the time-series data of the slip angle, regarding the tire which generates a tire lateral force by being brought into contact with a ground in a contact patch and rolling at a predetermined rolling speed; and (2) deriving a value of a tire dynamic element parameter representing the cornering characteristic of the tire by using: a transient response calculation model that is constituted by using at least one tire dynamic element parameter and is used to calculate output data corresponding to the lateral force data of a transient response generated in the tire with respect to the time-series data of the slip angle; and the acquired lateral force data.

In the above invention, it is preferable that the step of deriving the value of the tire dynamic element parameter is performed by using the time-series data of a transient response of the slip angle obtained by computing a convolution integral of a response function of a first-order-lag response of the transient response calculation model, which specifies a deformation response of a tread part of the tire during cornering, with a time gradient of the time-series data of the slip angle provided to the transient response calculation model.

Preferably, the step of acquiring the lateral force data is performed by reproducing an evaluation target tire with a tire finite element model, which is obtained by dividing the evaluation target tire into a finite number of elements, and by using a finite element method to acquire, as the lateral force data, simulation data of the lateral force acting on the tire finite element model which is brought into contact with the ground in the contact patch and caused to roll at the predetermined rolling speed and to which a time-series slip angle is input.

More preferably, the tire finite element model is coupled with a rim model for reproducing a rim, and reproduces the tire brought into contact with the ground in the contact patch and rolling at the predetermined rolling speed by bringing the tire finite element model into contact with a flat virtual road surface in the contact patch and moving the tire finite element model at the predetermined rolling speed relatively to the virtual road surface.

The tire finite element model preferably includes a reinforcement material portion corresponding to a cord reinforcing material of the tire, the reinforcement material portion having such a material characteristic that a stiffness along a tensile direction and a stiffness along a compression direction are different from each other.

It is more preferable that the tire finite element model is subjected to an inflation process for simulating tire inflation, and the inflation process is performed after one of an initial stress and an initial strain is applied to at least one portion of the tire finite element model.

Alternatively, in the invention, the step of acquiring the lateral force data is performed by providing a time-series slip angle to the tire while bringing the tire into contact with the ground in the contact patch and rolling the tire at the predetermined rolling speed, and by acquiring, as the lateral force data, measurement data of the time-series tire lateral force corresponding to the slip angle.

It is also preferable that the transient response calculation model is represented by setting a transient response of the tire lateral force with respect to the slip angle as a first-order-lag response; and the slip angle to be input ranges within such a linear range that the slip angle and the response of the tire lateral force with respect to the slip angle are in a substantially linear relation.

It is preferable that the step of deriving the value of the tire dynamic element parameter is performed by using the time-series data of the input slip angle and the time-series lateral force data corresponding to the time-series data of the slip angle in such a manner that the output data of the transient response calculation model matches the time-series lateral force data within an allowable range.

The slip angle may range from −2.0 degrees to 2.0 degrees. Then, it is preferable that when the output data is represented by F(t), the transient response calculation model contains a formula represented by Formula (A) described bellow; and the step of deriving the value of the tire dynamic element parameter includes obtaining a value of a cornering stiffness K_(y) and a value of a time constant t₃, which are dynamic element parameters of Formula (A) described bellow, by using the input time-series slip angle α(t) in such a manner that the F(t) within Formula (A) described bellow matches the time-series lateral force data F_(y)(t) corresponding to the slip angle α(t) within the allowable range.

$\begin{matrix} \text{[Mathematical~~Formula~~1]} & \; \\ {{F(t)} = {{K_{y} \cdot \tan}\left\{ {\int_{0}^{t}{\left\lbrack {1 - {\exp \left( {- \frac{t - t^{\prime}}{t_{3}}} \right)}} \right\rbrack \frac{{\alpha \left( t^{\prime} \right)}}{t^{\prime}}{t^{\prime}}}} \right\}}} & (A) \end{matrix}$

It is preferable that the output data calculated by the transient response calculation model comprises data of the tire lateral force transmitting to a wheel side via an equivalent stiffness K_(L) of an entirety of the tire with respect to an input of the slip angle; and when the predetermined rolling speed at a time of acquiring the lateral force data is assumed to be V, the step of deriving the value of the tire dynamic element parameter includes deriving a value of the equivalent stiffness K_(L) representing a transmission characteristic of the tire lateral force by substituting the value of the cornering stiffness K_(y) and the value of the time constant t₃, which are obtained by using the above-mentioned Formula (A), and the rolling speed V, into Formula (B) described bellow.

$\begin{matrix} \text{[Mathematical~~Formula~~2]} & \; \\ {t_{3} = \frac{K_{y}}{K_{L}V}} & (B) \end{matrix}$

The invention also provides an apparatus for evaluating a cornering characteristic of a tire under a condition in which a slip angle is provided as time-series data, comprising:

(1) a data acquiring section for acquiring time-series lateral force data with respect to a time-series slip angle, regarding the tire being brought into contact with a ground in a contact patch and rolling at a predetermined rolling speed; and (2) a deriving section for deriving a value of a tire dynamic element parameter representing the cornering characteristic of the tire by using: a transient response calculation model that is constituted by using at least one tire dynamic element parameter and is used to calculate output data corresponding to the lateral force data of a transient response generated in the tire with respect to the slip angle; and the lateral force data.

It is preferable that the deriving section derives the value of the tire dynamic element parameter by using the time-series data of a transient response of the slip angle obtained by computing a convolution integral of a response function of a first-order-lag response, which specifies a deformation response of a tread part of the tire during cornering, with a time gradient of the time-series data of the slip angle provided to the transient response calculation model.

In the present invention, time-series data of a transient response to a slip angle or a slip ratio of a tread part with respect to the road surface in a tire dynamic model is calculated through a convolution of a response function of a first-order-lag response which defines a deformation response of the tread part during cornering and the time gradient of time-series data of a slip angle given to the tire dynamic model and, based on the time-series data of the transient response to the slip angle, time-series data of a lateral force, a self-aligning torque, or a longitudinal force is calculated. Accordingly, time-series data in a transient state can readily be calculated with the use of a tire dynamic model.

A deformation response of the tread part which defines a transient response during cornering or braking/driving in a tire dynamic model is set as a first-order-lag response in the tire dynamic model. In calculating the value of a transient response parameter which determines the first-order-lag response, a value of the transient response parameter is initially set to fix a response function of the first-order-lag response, and the response function of the first-order lag and the time gradient of time-series data of a slip angle or a slip ratio are integrated in a convolution integral to obtain time-series data of a transient response to the slip angle of the tread part with respect to the road surface in the tire dynamic model. Accordingly, time-series data of a lateral force, a self-aligning torque, or a longitudinal force in a transient state during cornering or braking/driving can readily be calculated and the value of the transient response parameter can be searched for and determined with relative ease.

Furthermore, an actual constituent member of a tire, is associated with the value of a dynamics element parameter of a tire dynamic model, or the value of the transient response parameter, which makes it possible to design a tire that satisfies a desired condition about time-series data of a lateral force, a self-aligning torque, or a longitudinal force. Time-series data of a lateral force, a self-aligning torque, or a longitudinal force that is calculated by the tire transient response calculating method can be entered into a vehicle model to predict the motion of a vehicle during cornering or braking/driving.

A tire cornering characteristic evaluating method and evaluating device of the present invention obtains, as tire lateral force data, time-series measurement data equivalent to that of when a time-series slip angle is applied to an actual tire and, in addition, obtaining, as lateral force data, simulation data of a lateral force acting on a finite element model of a tire.

In obtaining measurement data of a lateral force of a tire, the rate of change of a slip angle input to the tire is set as the rate of change at which a slip angle changes in actual vehicle steering. The thus obtained cornering characteristic evaluation result is close to that of when a vehicle is actually steered. This also makes quantitative evaluation of a tire cornering characteristic possible while setting a range of a slip angle input to the tire to a relatively narrow range. Accordingly, it is possible to suppress tire degradation caused by the test, and the same tire can be evaluated multiple times for its cornering dynamic characteristic under different speed conditions.

When obtaining, as lateral force data, simulation data of a lateral force acting on a finite element model of a tire, an evaluation result equivalent to that of when a vehicle is actually steered can be obtained through a simulation that uses the finite element model without actually manufacturing a test tire.

The range of a slip angle input is set within a linear range where a slip angle input and a tire lateral force generated in response to the slip angle input have a substantially linear relation. This makes it possible to use a relatively simplified tire dynamic model (transient response calculation model) in which a cornering characteristic response to a slip angle input is represented by a first-order lag system. With such a relatively simplified transient response calculation model, the value of a tire dynamic element parameter indicating a tire cornering characteristic can be derived through relatively simple processing alone. Such information on a tire cornering characteristic obtained according to the present invention can be used favorably in, for example, development of a tire that improves the steering stability in high speed driving.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is a block diagram showing a computing device of an example for executing a tire transient response data calculating method and a data processing method according to the present invention;

FIG. 2 is a diagram for illustrating a tire dynamic model used in the tire transient response data calculating method and the data processing method according to the present invention;

FIG. 3 is a diagram for illustrating the tire dynamic model during cornering used in the tire transient response data calculating method and the data processing method according to the present invention;

FIGS. 4A to 4C are diagrams for illustrating the tire dynamic model used in the tire transient response data calculating method and the data processing method according to the present invention;

FIGS. 5A to 5C are diagrams for illustrating the tire dynamic model used in the tire transient response data calculating method and the data processing method according to the present invention;

FIGS. 6A to 6C are diagrams for illustrating the tire dynamic model used in the tire transient response data calculating method and the data processing method according to the present invention;

FIG. 7 is a diagram for illustrating a relationship between deformation of respective parts of the tire dynamic model used in the tire transient response data calculating method and the data processing method according to the present invention, and a torque and a lateral force;

FIGS. 8A to 8C are examples of time-series data acquired by actually measuring a tire, and FIGS. 8D to 8F are diagrams showing time-series data corresponding to FIGS. 8A to 8C, respectively, which is acquired by a tire transient response data calculating method according to the present invention;

FIGS. 9A and 9B are examples of time-series data acquired by actually measuring a tire, and FIGS. 9C and 9D are diagrams showing time-series data corresponding to FIGS. 9A and 9B, respectively, which are acquired by the tire transient response data calculating method according to the present invention;

FIG. 10 is a diagram for illustrating the tire dynamic model during braking/driving used in the tire transient response data calculating method and the data processing method according to the present invention;

FIGS. 11A and 11B are diagrams for illustrating how a longitudinal force is generated during braking/driving of a tire;

FIGS. 12A to 12C are diagrams for showing results acquired by the tire transient response data calculating method;

FIG. 13 is a flowchart showing a flow of an example of the tire transient response data calculating method according to the present invention;

FIGS. 14A and 14B are diagrams for illustrating a transient response of a slip angle used in the tire transient response data calculating method;

FIG. 15 is a flowchart showing a flow of an example of the data processing method according to the present invention;

FIG. 16 is a flowchart showing a flow of another example of the data processing method according to the present invention;

FIGS. 17A to 17D are graphs acquired by the method shown in FIG. 16;

FIG. 18 is a flowchart showing a flow of another example of the tire transient response data calculating method according to the present invention;

FIG. 19 is a schematic structural diagram for explaining a tire cornering characteristic evaluation device according to the present invention;

FIG. 20 is a schematic structural diagram for explaining a measurement/evaluation unit of the tire cornering characteristic evaluation device shown in FIG. 20;

FIGS. 21A and 21B are graphs each showing a time-series variation of a slip angle to be applied to a tire by a tire cornering characteristic measuring device shown in FIG. 20;

FIG. 22 is a flowchart of an example of a tire cornering characteristic evaluation method according to the present invention;

FIG. 23 is an example of results obtained by executing the tire cornering characteristic evaluation method according to the present invention, which is a graph showing results obtained by calculating respective time constants of two tires;

FIG. 24 is an example of results obtained by executing the tire cornering characteristic evaluation method according to the present invention, which is a plot diagram showing respective load dependencies of equivalent lateral stiffness of two tires;

FIG. 25 is another example of results obtained by executing the tire cornering characteristic evaluation method according to the present invention, which is a graph showing results obtained by calculating respective time constants of two tires;

FIG. 26 is another example of results obtained by executing the tire cornering characteristic evaluation method according to the present invention, which is a plot diagram showing respective load dependencies of equivalent lateral stiffness of two tires;

FIG. 27 is a schematic structural diagram for explaining another embodiment of the tire cornering characteristic evaluation device according to the present invention;

FIG. 28 shows an example of a tire finite element model created by the evaluation device shown in FIG. 27;

FIG. 29 is a diagram showing an example of a stress/strain curve of a carcass cord of a tire;

FIG. 30 is a graph showing a time-series variation of a slip angle applied to the tire finite element model by the tire cornering characteristic measuring device shown in FIG. 27; and

FIGS. 31A and 31B are plot diagrams showing a load dependencies of the equivalent lateral stiffnesses acquired by the evaluation device shown in FIG. 27.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A detailed description will be given below, with reference to the accompanying drawings, through a preferred embodiment of the present invention, of a tire transient response data calculating method, a data processing method, a tire designing method and a vehicle motion predicting method which use the tire transient response data calculating method, and a tire cornering characteristic evaluating method and device.

FIG. 1 is a block diagram of a computing device 10 which carries out a tire transient response data calculating method and a data processing method according to the present invention.

The computing device 10 is a device that receives an input of measurement data of a lateral force F_(y), a self-aligning torque (hereinafter simply referred to as torque) M_(z), and a longitudinal force F_(x) in a transient state when a slip angle or a slip ratio is given as time-series data to calculate a value of a lag time constant (transient response parameter), which characterizes a transient response characteristic of a tire, based on a tire dynamic model, which will be described later. The computing device 10 also calculates time-series data of the lateral force F_(y), the torque M_(z), and the longitudinal force F_(x) in a transient state by using the lag time constant and the values of tire dynamic element parameters that constitute the tire dynamic model. The term transient response characteristic refers to an output characteristic of the lateral force F_(y), the torque M_(z), and the longitudinal force F_(x) which change with time in accordance with changes with time of a slip angle or a slip ratio during cornering. The term transient response data refers to data of the lateral force F_(y), the torque M_(z), and the longitudinal force F_(x) in a transient state which change with time in accordance with changes with time of a slip angle or a slip ratio during cornering.

The computing device 10 is composed of: a data input section 12 which accepts various types of data including measurement data and parameters; a tire dynamic model computing section 14 which expresses a tire dynamic model described below in an analytical formula, and calculates a lateral force and a torque, or a longitudinal force, from set parameter values; a processing section 16 which has the tire dynamic model computing section 14 perform computation in a given sequence to determine the values of tire dynamic element parameters and various parameters of time lag constants (transient response parameters) described below, or which uses the tire dynamic model to calculate time-series data of a lateral force and a torque, or a longitudinal force, in a transient state; and an output section 18 which compiles the determined values of the lag time constants, or the calculated time-series data of the lateral force and the torque, or the calculated time-series data of the longitudinal force to output the resultant as output data to a monitor or printer (not shown).

The following are examples of tire dynamic element parameters calculated based on the tire dynamic model, which will be described later with reference to FIGS. 2, 3 and 10:

(a) A lateral stiffness K_(y0) defined by a lateral shear stiffness of a tire;

(b) A sliding friction coefficient μ_(d) between a road surface and a tire;

(c) A lateral stiffness coefficient (K_(y0)/μ_(s)) obtained by dividing the lateral stiffness K_(y0) by an adhesive friction coefficient μ_(s) between the road surface and the tire;

(d) A lateral bending compliance ε of a belt part;

(e) A torsional compliance (1/G_(mz)) corresponding to a reciprocal of a torsional stiffness about a tire center axis of the tire;

(f) A coefficient n for defining a contact pressure distribution on a contact patch when the lateral force is generated;

(g) A coefficient C_(q) indicating the degree of a bias in the contact pressure distribution;

(h) A shift coefficient C_(xc) indicating the degree of a longitudinal shift of the center position of the tire on the contact patch;

(i) An effective contact length l_(e) when the lateral force is generated;

(j) A longitudinal stiffness A_(x) (a parameter for defining a longitudinal torque component) in the contact patch;

and the like.

Examples of transient response parameters which characterize a transient response characteristic include:

(k) A lag time constant t_(s) of a first-order-lag response that defines a deformation response resulting from shear deformation of the tread part;

(l) A lag time constant t_(r) of a first-order-lag response that defines a deformation response resulting from torsional deformation of the side part; and

(m) A lag time constant t_(d) of a first-order-lag response that defines a deformation response resulting from bending deformation of the belt part.

Herein, the lateral stiffness K_(y0), the lateral bending compliance ε and G_(mz) of the torsional compliance (1/G_(mz)) are respectively a stiffness parameter against shear deformation of a tire, a stiffness parameter against lateral bending deformation, and a stiffness parameter against torsional deformation of the tire. The lag time constants of the above-mentioned items (k) to (m) represent time constants in response functions of the respective first-order-lag responses. A lateral direction in which the lateral force is generated designates an axial direction of a rotational axis of the tire. Therefore, in the case where the tire rolls to travel straight ahead, the lateral direction becomes identical with the right-left direction with respect to the travelling direction. On the other hand, in the case where the tire rolls at a slip angle, the lateral direction shifts with respect to the travelling direction of the tire by the slip angle. The longitudinal direction designates a direction, which is parallel to a road surface with which the tire comes into contact and perpendicularly crosses the axial direction of the rotational axis of the tire. A tire central axis (an axis CL of FIGS. 5A and 5B) is vertical to the road surface, perpendicularly crossing the rotational axis about which the tire rolls and passing on a central plane of the tire in a width direction.

The data input section 12 receives various data such as measurement data of a lateral force and a torque or, measurement data of a longitudinal force, and the above-mentioned parameters and rewrites those data in a predetermined format to supply those to the processing section 16. At the same time, various data thus input are stored in a memory 21.

The processing section 16 has the tire dynamic model computing section 14 compute a lateral force and a torque in accordance with a sequence described below, to thereby determine the values of various parameters, or calculates data of a lateral force, a torque, and a longitudinal force in a transient response state in the tire dynamic model.

The processing section 16 has four different sequences, and has components corresponding to the respective sequences. These components are: a cornering parameter calculating section 20 which determines the values of the above-mentioned lag time constants from measurement data of a lateral force and a torque; a braking/driving parameter calculating section 22 which determines the values of the above-mentioned lag time constants from measurement data of a longitudinal force; an F_(y)/M_(z) data calculating section 24 which obtains time-series data of a lateral force and a torque in a transient state by using the tire dynamic model; and an F_(x) data calculating section 26 which obtains time-series data of a longitudinal force in a transient state by using the tire dynamic model.

Functions of the cornering parameter calculating section 20, the braking/driving parameter calculating section 22, the F_(y)/M_(z) data calculating section 24, and the F_(x) data calculating section 26 will be described later.

The tire dynamic model computing section 14 is a computing section that uses various data supplied from the processing section 16 to obtain results of lateral force and torque computation and sends the obtained computation results to the processing section 16 in response.

FIGS. 2, 3, 4A to 4C, 5A to 5D and 6A to 6C are diagrams for illustrating the tire dynamic model.

The tire dynamic model is constructed to include, as shown in FIG. 2: a sidewall model composed of a plurality of spring elements representing a spring characteristic of a sidewall on an assumed rigid cylindrical member; a belt model made of an elastic ring body connected to the spring elements; and a tread model composed of an elastic element representing the tread model connected onto a surface of the elastic ring body.

The tire dynamic model that the tire dynamic model computing section 14 has calculates a lateral force and a torque in a transient state during cornering, or calculates a longitudinal force in a transient state during braking/driving, in accordance with instructions from the cornering parameter calculating section 20, the braking/driving parameter calculating section 22, the F_(y)/M_(z) data calculating section 24, and the F_(x) data calculating section 26.

The case of calculating a lateral force and a torque in a transient state during cornering is described first. As shown in FIG. 3, numerical values are set for tire dynamic element parameters composed of various linear parameters and non-linear parameters which are constructed by employing various spring elements of a tire, and then processed through Formulae (1) to (8) of FIG. 3 with the use of time-series data α(t) of a slip angle given as input data. A lateral force F_(y)(t) and a torque M_(z)(t) which are time-series data in Formulae (6) and (7) are thus calculated as data.

The term linear parameter refers to a parameter represented in a linear format in Formulae (6) and (7), and the term non-linear parameter refers to a parameter represented explicitly or implicitly in a non-linear format in Formulae (6) and (7).

[1−exp(−(t−t′)/t_(r))] in Formula (1) of FIG. 3 represents a response function of a first-order-lag response of torsional deformation caused in the side part by the torque M_(z)(t). [1−exp(−(t−t′)/t_(s))] in Formula (4) represents a response function of a first-order-lag response of shear deformation caused in the tread part by the given slip angle α(t). [1−exp(−(t−t′)/t_(d))] in Formula (8) represents a response function of a first-order-lag response of lateral bending deformation caused by a lateral force in the belt part.

The tire dynamic model computing section 14 calculates, through Formulae (1) containing the response function [1−exp(−(t−t′)/t_(r))] of a first-order-lag response, a recoil angle which is obtained from the torque M_(z)(t) and the torsional compliance (1/G_(mz)). The tire dynamic model computing section 14 subtracts the recoil angle from the given slip angle α(t), thereby calculating an effective slip angle α_(e)(t). A recoil angle caused by the torque M_(z)(t) is due to a first-order-lag response of torsional deformation of the side part. This recoil angle is calculated by multiplying the torsional compliance (1/G_(mz)) by the result of a convolution integral of the reference function of the first-order-lag response that defines the torsional deformation and the time gradient (time differential coefficient) of past time-series data of the torque M_(z)(t). In other words, the recoil angle is calculated by dividing the convolution integral result by the torsional stiffness. The effective slip angle α_(e)(t) is calculated in this way because the torque M_(z)(t) generated from the introduction of a slip angle works on the tire itself in a manner that the torque reduces the given slip angle. Accordingly, when the instruction of a slip angle generates the torque M_(z)(t), the effective slip angle α_(e)(t) and a corrected slip angle α_(f)(t) described below have a smaller value than that of the actually given slip angle α(t) as shown in FIG. 4A. The torque M_(z)(t) in Formula (1) is data of the torque M_(z)(t) in Formula (7) that is obtained in one preceding time step.

Furthermore, according to Formula (2), a bias coefficient q for defining the profile of distribution of a contact pressure is calculated from the torque M_(z). The bias coefficient q is a parameter indicating a profile of distribution of a contact pressure which is generated when the distribution of a contact pressure in a straight travelling state of the tire at the slip angle α=0 (see FIG. 5A) is biased by the generation of the lateral force F_(y) in a forward travelling direction (toward a leading edge on the contact patch) as shown in FIG. 5B. Assuming that the distribution of a contact pressure is p(x) (x is a position on the coordinates obtained by normalization with a contact length when an x-axis is defined in a backward travelling direction in FIGS. 5A and 5B), the profile of the distribution of the contact pressure p(x) is defined by a function D_(gsp) (x; n, q) expressed by Formula (9) of FIG. 5B.

Herein, a coefficient n in the function D_(gsp) (x; n, q) defines the distribution of the contact pressure on the contact patch while the lateral force is being generated, and defines the distribution of the contact pressure so that the distribution becomes more angular (a curvature becomes larger) in the vicinity of the leading edge and a trailing edge of the distribution of the contact pressure as shown in FIG. 5C. Moreover, as shown in FIG. 5D, as the coefficient q increases from 0 to 1, the position of a peak of the distribution of the contact pressure is set so as to shift toward the leading edge side. As described above, the coefficients q and n are profile defining coefficients for defining the distribution profile of the contact pressure.

Furthermore, according to Formula (3), a value (x_(c)/l) indicating the degree of a shift of the center position of the tire toward the leading edge when the lateral force F_(y) is generated is calculated in association with the torque M_(z). The value (X_(c)/1) is used in Formula (7). Herein, 1 is a contact length. The reason why a shift of the center position O of the tire is defined in Formula (3) is because the center position O serving as the center of rotation of the torque M_(z) shifts toward the leading edge on the contact patch due to the generation of the lateral force F_(y) as shown in FIG. 5B.

Through Formula (4), a slip angle in a transient state is defined with respect to the effective slip angle α_(e)(t) while taking into consideration the first-order-lag response of shear deformation of the tread part. Specifically, on the premise that the compliance to the road surface upon deformation of the tread part is based on the first-order-lag response, the result of a convolution integral of the reference function of the first-order-lag response that defines deformation of the tread part and the time gradient of the effective slip angle α_(e)(t) is defined as the corrected slip angle α_(f)(t) in a transient state. Formulae (5) to (7) each use the corrected slip angle α_(f)(t).

Furthermore, according to Formula (5), a boundary position (l_(h)/l) between a sliding friction and an adhesive friction in the contact patch, which occur at the large corrected slip angle α_(f)(t), is calculated. The boundary position (l_(h)/l) is defined in the following manner.

The maximum friction curves shown in FIGS. 6A to 6C are obtained by multiplying the adhesive friction coefficient us by the contact pressure distribution p(x). The tire tread part, which comes into contact with the road surface on its leading edge, is gradually sheared by the road surface due to the corrected slip angle α_(f)(t) as it moves toward the trailing edge. As a result, a shear force (adhesive frictional force) is generated from the tire tread part. If the shear force gradually increases to reach the maximum friction curve, the tire tread part, which is adhered to the road surface, starts sliding to generate a sliding frictional force in accordance with a sliding friction curve obtained by multiplying the sliding friction coefficient μ_(d) by the contact pressure distribution p(x). In FIG. 6A, the region on the leading edge side forward from the boundary position (l_(h)/l) is an adhesive region in which the tire tread part is adhered to the road surface, whereas the region on the trailing edge side is a tire sliding region in which the tire tread part slides on the road surface. FIG. 6B shows the state where the corrected slip angle α_(f)(t) is larger than that shown in FIG. 6A. The boundary position (l_(h)/l) moves toward the leading edge side as compared with FIG. 6A. If the corrected slip angle α_(f)(t) further increases, a sliding friction is generated at the position of the leading edge on the contact patch as shown in FIG. 6C.

As can be seen from FIGS. 6A to 6C, a ratio of the adhesive region and the sliding region greatly varies depending on the corrected slip angle α_(f)(t). A frictional force in the adhesive region and the sliding region as described above, that is, a lateral force component is integrated along a tire width direction, whereby the lateral force F_(y)(t) can be calculated. Furthermore, by calculating a moment about the tire center O, the torque M_(z)(t) can be calculated.

In the Formulae (6) and (7), the lateral force F_(y)(t) and the torque M_(z)(t) are calculated separately for the adhesive region and the sliding region described above by using the corrected slip angle α_(f)(t).

The Formula (6) calculates the lateral force F_(y)(t) by getting the sum of two terms (two lateral force components). The first term corresponds to the integration within the integral range of 0 to (l_(h)/l), representing an adhesive lateral force component generated in the adhesive region. The second term corresponds to the integration within the integral range of (l_(h)/l) to 1, representing a sliding lateral force component generated in the sliding region.

The adhesive lateral force component of the first term in Formula (6) is a lateral force in the adhesive region. Formula (6) represents a state in which a lateral displacement of the tread part due to the corrected slip angle α_(f)(t) is delayed by lateral bending deformation of the belt, to thereby calculate the adhesive lateral force component. The sliding lateral force component of the second term in Formula (6) is a lateral force in the sliding region. Formula (6) expresses the profile of the contact pressure distribution p(x) caused by the corrected slip angle α_(f)(t) by the function D_(gsp)(x; n, q) to calculate the sliding lateral force component.

In Formula (7), the first term corresponds to the integration within the integral range of 0 to (l_(h)/l), representing a torque component generated by the adhesive lateral force component generated in the adhesive region. The second term corresponds to the integration within the integral range of (l_(h)/l) to 1, representing a torque component generated by the sliding lateral force component generated in the sliding region. In Formula (7), in addition to the above-mentioned two torque components, another torque component, that is, a third term is provided. The third term, A_(x)·(l_(h)/l)·tan α_(f)(t), represents a torque component about the tire center O, which is generated by the amount of a shift of the contact patch of the tire and a longitudinal force of the tire when the contact patch of the tire has a lateral shift due to the presence of the slip angle α as described below. More specifically, the torque M_(z)(t) is calculated by the sum of three torque components, i.e., the torque component generated by the adhesive lateral force, the torque component generated by the sliding lateral force, and the torque component generated by the longitudinal force.

Formula (8) is a formula that defines F_(ye)(t), which represents a corrected lateral force as a result of the belt part receiving lateral bending deformation from the lateral force F_(y)(t). The lateral force correction in Formula (8) employs convolution integral of a response function of a first-order-lag response of lateral bending deformation of the belt part and the time gradient of past time-series data of the lateral force F_(y)(t).

The tire dynamic model computing section 14 sequentially calculates through Formulae (1) to (8) time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) while increasing the time in increments of infinitesimal time Δt from t=0. Accordingly, the lateral force F_(ye)(t) that is obtained through Formula (8) in a time step at a time t is used as F_(ye)(t) in Formulae (5) and (6) in the next time step, i.e., a time (t+Δt). Similarly, the torque M_(z)(t) that is obtained through Formula (7) at the time t is used as M_(z)(t) in Formulae (1), (2), (3), and (4) in the next time step (time t+Δt).

FIGS. 4A to 4C are a schematic representation of the contact patch showing the relation between the delayed adhesive lateral force component and longitudinal component and the torque component which is caused by the corrected slip angle α_(f)(t) and deformation of the belt.

FIG. 4A shows a state in which, when time-series data of the slip angle α(t) is given, the slip angle α(t) works on the tire itself such that a torque generated by the slip angle α(t) reduces the slip angle α(t), and becomes the corrected slip angle α_(f)(t) in a transient state due to first-order lag deformation. FIG. 4B shows the relation between lateral displacement that is caused by this corrected slip angle α_(f)(t) and lateral displacement that is caused by lateral bending deformation of the belt. FIG. 4C shows a mechanism of how the distribution of a longitudinal force that is generated by a lateral shift of the contact patch of the tire due to a lateral force contributes to the torque M_(z)(t). In FIG. 4C, M_(z1) and M_(z2) indicate the torque component that is generated by the adhesive lateral force component and the torque component that is generated by the sliding lateral force component, respectively, whereas M_(z3) indicate the torque component that is generated by the longitudinal force acting on the contact patch.

FIG. 7 is a processing block diagram showing steps from the introduction of the slip angle α(t) up through calculation of the lateral force F_(y)(t) and the torque M_(z)(t). When the lateral force F_(y)(t) and the torque M_(z)(t) are calculated through Formulae (6) and (7), as can be seen in FIG. 7, in the tire dynamic model according to the present invention, lateral bending deformation of the belt part, a change in profile of the contact pressure distribution, and torsional deformation of the side part affect the calculation of the lateral force F_(y)(t) and the torque M_(z)(t). In addition, lateral bending deformation of the belt part, torsional deformation of the side part, and shear deformation of the tread part are expressed by first-order-lag responses. G₁(s), G₂(s), and G₃(s) of FIG. 7 are the Laplace transform representation of transfer functions of the above-mentioned first-order-lag responses, and s denotes a Laplace operator.

In general, when a lag time constant related to transient responsiveness of a tire is given as t_(x), the lag time constant t_(x) is often handled in the form of a relaxation length σ_(x) by taking into account the dependency on a travelling speed V. The relaxation length σ_(x) means “a travelling distance necessary for a tire to output a steady-state lateral force when a slip angle is input in a step-wise manner”. The lag time constant t_(x) of a transient response at the travelling speed V is expressed as follows:

t _(x)=σ_(x)(relaxation length)/V(travelling speed)

Relaxation lengths σ_(s), σ_(d), and σ_(r) are defined for the lag time constants t_(s), t_(r), and t_(d), respectively. With the relaxation length and a distance frequency S_(v)=s/V, the transfer function in the block diagram of FIG. 7 can be expressed in the following format from which the dependency on the travelling speed is eliminated:

$\begin{matrix} {{{G_{1}\left( s_{v} \right)} = \frac{K_{yo}}{1 + {\sigma_{s} \cdot s_{v}}}}{{G_{2}\left( s_{v} \right)} = {\frac{ɛ\; 1_{e}}{3} \cdot \frac{1}{1 + {\sigma_{d} \cdot s_{v}}}}}{{G_{3}\left( s_{v} \right)} = {\frac{1_{e}}{6G_{m\; z}} \cdot \frac{1}{1 + {\sigma_{r} \cdot s_{v}}}}}} & \left\lbrack {{Mathematical}\mspace{14mu} {Formula}\mspace{20mu} 5} \right\rbrack \end{matrix}$

Other formulae in the model according to the present invention can also be converted through a descriptive format conversion similar to the above-mentioned conversion (t_(x)→σ_(x)).

The lateral force F_(ye)(t) calculated in the tire dynamic model computing section 14 does not always match the lateral force F_(y)(t). However, since the time step of the lateral force F_(ye)(t) and the time step of the lateral force F_(y)(t) are one step ahead or behind of each other, the difference between the lateral force F_(ye)(t) and the lateral force F_(y)(t) is small enough to deem their values substantially equal to each other.

While this embodiment uses shear deformation of the tread part, lateral bending deformation of the belt part, and torsional deformation of the side part as separate first-order-lag responses, in the present invention at least shear deformation of the tread part may be used as a first-order-lag response. The lag time constant in shear deformation of the tread part is longer than those in lateral bending deformation of the belt part and torsional deformation of the side part, and serves as the major factor of a tire cornering transient response.

The values of linear and non-linear parameters including dynamics element parameters that are used in the tire dynamic model are stored in advance in the memory 21. The values of these parameters are obtained by, for example, a parameter value deriving method disclosed in JP 2005-88832 A.

FIGS. 8A to 8F show a comparison between the lateral force F_(y)(t) and the torque M_(z)(t) that are obtained by actual measurement of a tire and the lateral force F_(y)(t) and the torque M_(z)(t) that are calculated in the tire dynamic model. In an example of FIGS. 8A to 8C, the slip angle α(t) is given as time-series data to a tire (the tire size: 205/55R16 89V) under such conditions that sets the travelling speed to 80 (km/hour) and the load to 3.9 (kN), and measurement data shown in FIGS. 8B and 8C are obtained for the lateral force F_(y)(t) and the torque M_(z)(t). Corresponding time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) that are calculated with the use of the tire dynamic model are shown in FIGS. 8E and 8F. FIG. 8D shows time-series data of the slip angle α(t) given to the tire dynamic model.

FIGS. 9A and 9B are graphs having the slip angle α(t) as the axis of abscissa to show the measurement data of FIGS. 8A to 8C. The tire dynamic model uses only the lag time constant t_(s) in shear deformation of the tread part as a transient response (t_(s)=0.03 second), and does not use the lag time constants in lateral bending deformation of the belt part and torsional deformation of the side part. Graphs of the corresponding lateral force F_(y)(t) and torque M_(z)(t) that are calculated with the use of the tire dynamic model are shown in FIGS. 9C and 9D.

Comparing the graphs corresponding to FIGS. 8A to 8F and FIGS. 9A to 9D, it is found that the lateral force F_(y)(t) and the torque M_(z)(t) that are calculated using the tire dynamic model are extremely approximate to the actually measured measurement data, and time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) of a transient response during cornering can be calculated using the tire dynamic model so as to correspond to the actual measurement. In the examples of FIGS. 8D to 8F and FIGS. 9C and 9D, the dynamic element parameter values obtained in advance based on the measurement data of the lateral force F_(y) and the torque M_(z) in a steady state were used. The dynamic element parameter values were obtained by using a method of deriving numerical values of parameters disclosed in JP 2005-88832 A.

Next, a tire dynamic model in a case where a longitudinal force in a transition state during braking/driving is calculated will be described.

As shown in FIG. 10, tire dynamic element parameter values containing various linear parameters and non-linear parameters combined by various spring elements of a tire are set, and time-series data S(t) of a slip ratio given as input data is used to calculate the longitudinal force F_(x)(t) which is time-series data in Formula (14) processed according to Formulae (10) to (14) of FIG. 10.

The time-series data of the longitudinal force is sequentially calculated by increments of infinitesimal time Δt from t=0. Here, [1−exp(−(t−t′)/t_(r))] in Formula (11) represents a response function of a first-order-lag response of shear deformation of the tread part which is caused at the given slip ratio S(t).

The linear parameter of FIG. 10 indicates a parameter represented in Formula (14) in a linear form, and the non-linear parameter indicates a parameter represented explicitly or implicitly in Formula (14) in a non-linear form.

The tire dynamic model computing section 14 calculates a corrected slip ratio S_(f)(t) based on Formula (11) represented using the response function [1−exp(−(t−t′)/t₅)] of the first-order-lag response.

Specifically, the first-order-lag response is caused due to a first-order lag of the shear deformation of the tread part in a longitudinal direction. It is assumed that a result obtained by computing a convolution integral of the response function of the first-order-lag response specifying a deformation response at that time with the time gradient of the past time-series data of the slip ratio S(t) is set as the corrected slip ratio S_(f)(t). The corrected slip ratio S_(f)(t) acts on the belt part.

Further, according to Formula (10), a bias coefficient q specifying a shape of a contact pressure distribution is calculated from the torque M_(z). The bias coefficient q is, similar to that of the tire dynamic model during cornering shown in FIG. 3, a parameter representing the contact pressure distribution which is generated when the contact pressure distribution (see FIG. 5A) in a state of straight-ahead travelling at the slip ratio S=0 is biased by the generated longitudinal force F_(x) toward the front in the travelling direction (leading edge on a contact patch) as shown in FIG. 5B. Assuming that the contact pressure distribution is p(x) (where x is a position on coordinates normalized by a contact length in a case where an x-axis is obtained toward the backward direction in the travelling direction in FIGS. 5A and 5B), the shape of the contact distribution p(x) is specified as a function D_(gsp) (x; n, q) represented by Formula (9) of FIG. 5B.

In this case, a coefficient n in the function D_(gsp) (x; n, q) specifies the contact pressure distribution in the contact patch while the lateral force is being generated, and specifies the contact pressure distribution such that the contact pressure distribution becomes more angular (a curvature becomes larger) in the vicinities of the leading edge and the trailing edge as shown in FIG. 5C. As shown in FIG. 5D, the peak position of the contact pressure distribution is set so as to move toward the leading edge side as the coefficient q varies from 0 to 1. Thus, the coefficients q and n are profile defining coefficients for defining the profile of the contact pressure distribution.

Further, according to Formula (12), a boundary position (l_(h)/l) between a sliding friction and an adhesive friction in the contact patch, which occur at the large slip ratio S_(f)(t), is calculated. The boundary position (l_(h)/l) is defined in the following manner.

FIGS. 11A and 11B are explanatory diagrams of the longitudinal force which is generated in a tire.

As shown in FIG. 11A, the tread part, which comes into contact with the road surface on its contact patch leading edge, moves toward the contact patch trailing edge at a tread rolling speed V_(t), while the road surface which comes into contact with the tire upon braking moves backward at a tire travelling speed V_(p) which is higher than the tread rolling speed V_(t). Since the tread rolling speed V_(t) is lower than the tire travelling speed V_(p), the tread part receives larger shear force in the backward direction of the travelling direction by the speed difference V_(p)−V_(t) as the tread part moves toward the backward direction from the leading edge of the contact patch. When the shear force is smaller than the maximum adhesive frictional force between the tread and the ground, relative movements of the tread and the ground do not occur, and the tread part is in an adhesive friction state. If the shear force exceeds the maximum adhesive frictional force, the tread part starts moving relatively with respect to the ground and is in a sliding frictional state. A braking force is represented by a frictional force obtained by summing up frictional forces in the adhesive region and frictional forces in the sliding region that are generated in the contact patch. The entire braking force obtained by summing up the frictional forces is divided by a load applied to a tire, thereby obtaining a braking force coefficient μ.

The maximum adhesive frictional force specifies a boundary between an adhesive friction and a sliding friction, and becomes an important factor characterizing a p-S curve. As shown in FIG. 11B, the maximum adhesive frictional force can be schematically represented by a product of the contact pressure distribution p(x) which is a distribution of contact pressures in the rotational direction of the tire (direction in which a braking force is received) and an adhesive frictional coefficient μ_(s). The contact pressure distribution p(x) is the same as the contact pressure distribution p(x) shown in FIG. 5B.

Thus, when the shear force acting on the tread part gradually increases to reach the maximum frictional curve, the tread part, which has been adhered to the road surface, starts sliding to generate a sliding frictional force in accordance with a sliding frictional curve obtained by multiplying the sliding friction coefficient μ_(d) by the contact pressure distribution p(x). In FIG. 11B, the region on the leading edge side ranging from the boundary position (l_(h)/l) to the leading edge is an adhesive region in which the tire tread member is adhered to the road surface, while the region on the trailing edge side is a sliding region in which the tread part slides on the road surface.

As apparent from FIG. 11B, a ratio between the adhesive region and the sliding region varies to a large extent according to the corrected slip ratio S_(f)(t). The longitudinal force F_(x)(t) can be calculated by integrating the frictional forces in the adhesive region and in the sliding region, that is, longitudinal force components, along the longitudinal direction of the tire.

According to Formula (14), the longitudinal force F_(x)(t) is calculated using the corrected slip ratio S_(f)(t) for each of the above-mentioned adhesive region and sliding region.

According to Formula (12), the boundary position (l_(h)/l) between the sliding frictional force and the adhesive frictional force in the contact patch, which occur at the large slip ratio S_(f)(t), is calculated.

The Formula (13) defines a sliding frictional coefficient μ_(d), and specifies the sliding frictional coefficient μ_(d) to depend on the travelling speed V_(p).

According to Formula (14), the longitudinal force F_(x)(t) is represented by a sum of the adhesive frictional force and the sliding frictional force.

The linear or non-linear parameter values including dynamic element parameters used for the tire dynamic model are stored in a memory 21 in advance. Those parameter values can be obtained by using a method of deriving numerical values of parameters disclosed in, for example, JP 2003-57134 A.

FIGS. 12A to 12C show calculation results of the longitudinal force F_(x)(t) calculated by the tire dynamic model. In the examples of FIGS. 12A to 12C, when a tire (tire size is 205/55R16 94V) is given with the slip ratio S(t) as time-series data under conditions of a travelling speed of 80 (km/h) and a load of 3.9 (kN), the longitudinal forces F_(x)(t) shown in FIGS. 12B and 12C are calculated. A lag time constant t_(s) of this case is set to 0.035 seconds.

FIG. 12A shows two types of slip ratios S(t) given to the tire dynamic model, that is, one having a sine wave of 0.5 Hz and the other having a sine wave of 2 Hz. FIG. 12B is a graph showing a locus obtained in a case where the longitudinal force F_(x)(t) equivalent to 1.5 cycles of the slip ratio S(t) with the sine wave of 0.5 Hz is divided by a load F_(z) (=3.9 kN). FIG. 12B also shows the longitudinal force F_(x) in a steady state for comparison. Thus, at the slip ratio S(t) with the sine wave of 0.5 Hz, the longitudinal force F_(x)(t) changes from the longitudinal force F_(x) in the steady state. FIG. 12C is a graph showing a locus obtained in a case where the longitudinal force F_(x)(t) equivalent to 1.5 cycles of the slip ratio S(t) with the sine wave of 2 Hz is divided by the load F_(z) (=3.9 kN). FIG. 12C also shows the longitudinal force F_(x) in the steady state for comparison. Thus, at the slip ratio S(t) with the sine wave of 2 Hz, the longitudinal force F_(x)(t) changes from the longitudinal force F_(x) in the steady state, and changes to a large extent as compared with the longitudinal force at the slip ratio S(t) with the sine wave of 0.5 Hz. Thus, in the tire dynamic model, it is found that the longitudinal force F_(x)(t) also changes according to the frequency of the slip ratio S(t). The dynamic element parameter values of the tire dynamic model are obtained by using the method of deriving numerical values of parameters disclosed in JP 2003-57134 A.

Thus, as shown in FIG. 3, the tire dynamic model computing section 14 calculates the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) by giving the time-series data of the slip angle α(t). On the other hand, as shown in FIG. 10, the tire dynamic model computing section 14 calculates the time-series data of the longitudinal force F_(x)(t) by giving the time-series data of the slip ratio S(t). The time-series data of the lateral force F_(x)(t) and the torque M_(z)(t) or the time-series data of the longitudinal force F_(x)(t) is output to the cornering parameter calculating section 20, the braking/driving parameter calculating section 22, the F_(y)/M_(z) data calculating section 24, and the F_(x) data calculating section 26, and each processing is performed.

Next, functions of the cornering parameter calculating section 20, the braking/driving parameter calculating section 22, the F_(y)/M_(z) data calculating section 24, and the F_(x) data calculating section 26 will be described.

The cornering parameter calculating section 20 supplies the tire dynamic model computing section 14 with the given time-series data of the slip angle α(t) and initialized values of lag time constants t_(s), t_(r), and t_(d). The tire dynamic model computing section 14 calculates the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) according to Formulae (1) to (8) shown in FIG. 3, by using the supplied slip angle α(t), the initialized values of the lag time constants t_(s), t_(r), and t_(d), and the parameter values loaded from the memory 21, and returns the time-series data to the cornering parameter calculating section 20. In a case where the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) calculated by the tire dynamic model computing section 14 is compared with the measurement data of the lateral force F_(y)(t) and the torque M_(z)(t) that are separately measured and stored in the memory 21, in other words, a case where a sum of square residuals between the calculated lateral force F_(y)(t) and torque M_(z)(t), and the actually measured lateral force F_(y)(t) and torque M_(z)(t) is obtained, and when the sum of square residuals is not smaller than a predetermined value, the cornering parameter calculating section 20 corrects the initialized values of the lag time constants t_(s), t_(r), and t_(d). Then, the corrected values and the slip angle α(t) are supplied to the tire dynamic model computing section 14 again, and the calculation of the lateral force F_(y)(t) and the torque M_(z)(t) is repeated. Thus, until the sum of square residuals becomes smaller than the predetermined value and becomes minimum, the values of the lag time constants t_(s), t_(r), and t_(d) are repeatedly corrected. Then, the value of the lag time constant obtained when the sum of square residuals becomes minimum is determined as a value of a lag time constant for defining the first-order-lag response.

Thus, the cornering parameter calculating section 20 determines the value of the lag time constant.

The sum of square residuals calculated for the value of the lag time constant may be calculated using only the lateral force F_(y)(t), may be calculated using only the torque M_(z)(t), or may be calculated using both the lateral force F_(y)(t) and the torque M_(z)(t).

The braking/driving parameter calculating section 22 supplies the tire dynamic model computing section 14 with the given slip ratio S(t) and the value initialized as the lag time constant t_(s). The tire dynamic model computing section 14 calculates the time-series data of the longitudinal force F_(x)(t) according to Formulae (10) to (14) shown in FIG. 10, by using the supplied slip ratio S(t), the lag time constant t_(s), and the parameter values loaded from the memory 21, and returns the time-series data to the braking/driving parameter calculating section 22. In a case where the time-series data of the longitudinal force F_(x)(t) calculated by the tire dynamic model computing section 14 is compared with the measurement data of the longitudinal force F_(x)(t) which is obtained by a separate measurement of the tire and stored in the memory 21, in other words, a case where a sum of square residuals between the calculated longitudinal force F_(x)(t) and the actually measured longitudinal force F_(x)(t) is obtained, and when the sum of square residuals is not smaller than a predetermined value, the braking/driving parameter calculating section 22 corrects the initialized value of lag time constant t_(s). Then, the corrected value and the slip ratio S(t) are supplied to the tire dynamic model computing section 14 again, and the calculation of the longitudinal force F_(x)(t) is repeated. Thus, until the sum of square residuals becomes smaller than the predetermined value and becomes minimum, the value of the lag time constant t_(s) is repeatedly corrected. Then, the value of the lag time constant t_(s) obtained when the sum of square residuals becomes minimum is determined as a value of a lag time constant for defining the first-order-lag response.

Thus, the braking/driving parameter calculating section 22 determines the value of the lag time constant.

The cornering parameter calculating section 20 and the braking/driving parameter calculating section 22 calculate, in the tire dynamic model, the lateral force F_(y)(t), the torque M_(z)(t), and the longitudinal force F_(x)(t) by using known values of the linear parameter and the non-linear parameter in the steady state, to thereby determine the value of the lag time constant. According to the present invention, at least a part of the linear parameter and the non-linear parameter may be set to be unknown values, to thereby determine the unknown values as well as the value of the lag time constant.

The F_(y)/M_(z) data calculating section 24 supplies the time-series data of the slip angle α(t) to the tire dynamic model computing section 14 to cause the tire dynamic model computing section 14 to calculate the lateral force F_(y)(t) and the torque M_(z)(t) by using the parameter values and the values of the lag time constants t_(s), t_(r), and t_(d) that are stored in the memory 21, thereby obtaining the data as time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) in a transient state during cornering.

The F_(x) data calculating section 26 supplies the time-series data of the slip ratio S(t) to the tire dynamic model computing section 14, to cause the tire dynamic model computing section 14 to calculate the longitudinal force F_(x)(t) by using the parameter values and the value of the lag time constant t_(s) that are stored in the memory 21, thereby obtaining the data to time-series data as the longitudinal force F_(x)(t) in a transient state during braking/driving.

The computing device 10 has the configuration as described above.

FIG. 13 shows a tire transient response data calculating method, that is, a flowchart showing a flow of calculating time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) during cornering, or time-series data of the longitudinal force F_(x)(t) during braking/driving. Calculation of the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) during cornering is mainly described below, and calculation of time-series data of the longitudinal force F_(x)(t) during braking/driving is described in parentheses.

First, in the F_(y)/M_(z) data calculating section 24 (F_(x) data calculating section 26), the slip angle α(t) (slip ratio S(t)) is set (Step S10). Settings of the slip angle α(t) (slip ratio S(t)) may be input by an input operation system such as a mouse or a keyboard connected to the computing device 10, or may be created by the computing device 10. Alternatively, the settings may be input from an external device connected to the computing device 10. For example, the time-series data of the slip angle α(t) as shown in FIG. 8D is set. The time-series data is supplied to the tire dynamic model computing section 14.

In the tire dynamic model computing section 14, the linear parameter values used for the tire dynamic model and the non-linear parameter values including the value of the lag time constant, which are stored in the memory 21, are loaded and are obtained as the parameter values of the tire dynamic model (Step S20).

In the tire dynamic model computing section 14, those parameter values are used together with the supplied slip angle α(t) (slip ratio S(t)) to calculate the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) according to Formulae (1) to (8) (Formulae (10) to (14)) (Step S30). The time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) calculated in the tire dynamic model computing section 14 is returned to the F_(y)/M_(z) data calculating section 24 (F_(x) data calculating section 26) and set as the time-series data during cornering (braking/driving).

The present invention is characterized in that response functions of a first-order-lag response used for the tire dynamic model are represented by [1−exp(−(t−t′)/t_(r))], [1−exp(−(t−t′)/t_(s))], and [1−exp(−(t−t′)/t_(d))], computation of a convolution integral of these response functions with a time gradient of the time-series data of the torque M_(z)(t), an effective slip angle α_(e)(t), and a lateral force F_(y)(t) is performed, and the obtained value is used for the tire dynamic model. Through the convolution integration, the slip angle (slip ratio) during cornering (braking/driving) forms a curve which gradually changes, and the time-series data substantially equal to the actually measured measurement data can be calculated as shown in FIG. 8. FIG. 14A shows an example where the effective slip angle α_(e)(t) is a step function. In this case, through the computation of the convolution integral of the response function with the time gradient of the time-series data, a corrected slip angle α_(f)(t) representing a curve which gradually changes as shown in FIG. 14B.

FIG. 15 is a flowchart showing an example of the data processing method according to the present invention. The data processing method is used in the computing device 10 for determining a value of a lag time constant (relaxation time constant) of a response function for defining a transient response during cornering or braking/driving. Determination of the lag time constant in a first-order-lag response during cornering is mainly described below, and determination of the lag time constant in a first-order-lag response during braking/driving is described in parentheses.

First, in the cornering parameter calculating section 20 (braking/driving parameter calculating section 22), time-series data of the slip angle α(t) (slip ratio S(t)) is set (step S110). Settings of the slip angle α(t) (slip ratio S(t)) may be input by an input operation system such as a mouse or a keyboard connected to the computing device 10, or may be created by the computing device 10. Alternatively, the settings may be input from an external device connected to the computing device 10. For example, the time-series data of the slip angle α(t) as shown in FIG. 8D is set. The time-series data is supplied to the tire dynamic model computing section 14.

The set series-data of the slip angle α(t) (slip ratio S(t)) is supplied to a tire behavior testing machine such as a cornering characteristic measuring device (FIG. 19) to test the tire based on the time-series data of the supplied slip angle α(t) (slip ratio S(t)). Thus, the actual measurement of the tire is performed, the measurement data of the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) in a transient state is obtained (Step S120). The obtained measurement data is supplied to the computing device 10 and stored in the memory 21.

Then, in the cornering parameter calculating section 20 (braking/driving parameter calculating section 22), the values of the linear parameter and the non-linear parameter that are stored in the memory 21 are loaded, and are obtained as parameters to be used for the tire dynamic model (step S130).

Then, in the cornering parameter calculating section 20 (braking/driving parameter calculating section 22), lag time constants (relaxation time constant) t_(r), t_(s), and t_(d) (lag time constant t_(s)) for specifying the response function of the first-order-lag response of the tire are initialized to a predetermined value, for example, 0.02 seconds (Step S140).

After that, the initialized values of the lag time constants t_(r), t_(s), and t_(d) (lag time constant t_(s)) set in the cornering parameter calculating section 20 (braking/driving parameter calculating section 22) and the set time-series data of the slip angle α(t) (slip ratio S(t)) are supplied to the tire dynamic model computing section 14.

In the tire dynamic model computing section 14, the linear parameter value and the non-linear parameter values except the lag time constant, which are stored in the memory 21, are loaded, and the parameter values and the values of the lag time constant are used together with the supplied time-series data of the slip angle α(t) (slip ratio S(t)), to thereby calculate the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) according to Formulae (1) to (8) (Formulae (10) to (14)) (Step S150).

The calculated lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) are returned to the cornering parameter calculating section 20 (braking/driving parameter calculating section 22), and the measurement data of the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) that are actually measured in Step S120 and stored in the memory 21 are loaded to calculate a sum of square residuals between the calculated time-series data of the lateral force F_(y)(t) and the calculated time-series data of the torque M_(z)(t) (longitudinal force F_(x)(t)) (Step S160). The sum of square residuals is calculated by obtaining a difference between the lateral forces F_(y)(t) and a difference between the torques M_(z)(t) at the same time of the time-series data then making each difference squared and summing up. Thus, when the sum of square residuals is smaller than a predetermined value which is approximate to 0, the calculated time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) is assumed to be substantially equal to the actual measurement data.

As a result, it is judged whether or not the sum of square residuals is smaller than the predetermined value and is a minimum value (Step S170).

When the judgement result shows that the sum of square residuals is not smaller than the predetermined value or is not a minimum value, the set values of the lag time constants t_(r), t_(s), and t_(d) (lag time constant t_(s)) are corrected (Step S180). When the judgement result shows that the sum of square residuals is smaller than the predetermined value and is a minimum value, the set values of the lag time constants are determined as lag time constants of the response function representing the first-order-lag response (Step S190). A method of minimizing the sum of square residuals is not particularly limited, and a non-linear least-squares regression algorithm of the Newton-Raphson method may be adopted.

Thus, the measurement data in a transient state during cornering (braking/driving) of the tire is acquired in advance by providing the tire with the time-series data of the slip angle (slip ratio) as measurement conditions, while, after the lag time constant is initialized, the lateral force F_(y)(t) and the torque M_(z)(t) (longitudinal force F_(x)(t)) are calculated using the tire dynamic model. Then, the sum of the square residuals between the measurement data of the tire and the calculated time-series data is calculated. When the sum of the square residuals is not acceptable, the value of the lag time constant is corrected and the calculation is repeated until the sum of square residuals becomes minimum, thereby determining the set value of the lag time constant obtained when the sum of square residuals is minimum as a value of the lag time constant for defining the first-order-lag response. At this time, the linear parameter value and the non-linear parameter values except the lag time constant that are used for the tire dynamic model are calculation results which originates from the lateral force F_(y) and the torque M_(z) (longitudinal force F_(x)) in the steady state. The lag time constant in the transient response can be determined by using tire dynamic element parameter values in the steady state, thereby making it possible to determine the lag time constant with efficiency.

According to the present invention, the value of the lag time constant can be determined not only in the flow of FIG. 15, but also by the following method. FIG. 16 is a flowchart of determining the value of the lag time constant (relaxation time constant) by a method different from that shown in FIG. 15. FIGS. 17A to 17D show graphs for explaining the data processing method.

In the following description, the transient response data during cornering when the time-series data of the slip angle is given to the tire dynamic model will be described, but the transient response during braking/driving when the time-series data of the slip ratio is given can also be described in the same manner. Hereinafter, the transient response during cornering is mainly described, and the transient response during braking/driving is described in parentheses. Specifically, in the data processing method to be described below, a deformation response of the tread part for specifying the transient response during cornering (braking/driving) in the tire dynamic model constituted by using a tire dynamic element parameter (a lag time constant) is set as a first-order-lag response to calculate a value of a transient response parameter (a lag time constant) for defining the first-order-lag response.

First, in the cornering parameter calculating section 20 (braking/driving parameter calculating section 22), time-series data of the slip angle (slip ratio), which varies across at least a range between 0 degrees and a predetermined angle (slip ratio between 0 and the predetermined value) while the slip angle (slip ratio) reciprocates, is set (step S210). For example, as shown in FIG. 17A, time-series data of a slip angle which varies while reciprocating between −20 degrees and +20 degrees is set.

Next, by giving the set time-series data of the slip angle α(t) (slip ratio S(t)) as a measurement condition to the tire, the transient response data during cornering (braking/driving) of the tire is actually measured, to thereby obtain in advance the measurement data of the lateral force F_(y)(t) or the torque M_(z)(t) (longitudinal force F_(x)(t)) at that time (step S220). For example, measurement data of the actually measured lateral force F_(y)(t) as shown in FIG. 17 is obtained. The measurement of the tire was conducted under measurement conditions of a tire size of 205/55R16 89V, a load of 3.9 (kN), and a travelling speed of 80 (km/h).

While the transient response data during cornering (braking/driving) is actually measured, the lag time constant (relaxation time constant) of the deformation response of the first-order lag in the entire tire that is used for the tire dynamic model is set as t₁, and the value of t₁ is initialized to define the response function of the first-order-lag response (Step S240).

Then, the tire dynamic model computing section 14 performs computation of a convolution integral of the defined response function of the first-order lag with the time gradient of the slip angle (slip ratio) to calculate a corrected slip angle α′(t) (corrected slip ratio S′(t)) which is time-series data of a transient response of a slip angle (slip ratio) in the tread part with respect to the road surface in the tire dynamic model according to Formula (20) (where C=t′) described bellow (Step S250).

The calculated value of the time-series data of the transient response of the corrected slip angle α′(t) (corrected slip ratio S′(t)) is returned to the cornering parameter calculating section 20 (braking/driving parameter calculating section 22) to be set as the value of the time-series data of the transient response, and then a characteristic curve represented by the value of the time-series data of the transient response of the corrected slip angle α′(t) (corrected slip ratio S′(t)) and the value of the actually measured lateral force F_(y)(t) or torque M_(z)(t) (longitudinal force F_(x)(t)) obtained in Step S120 is formed. The characteristic curve is a curve obtained when the slip angle (slip ratio) is represented on the horizontal axis and the lateral force or torque (longitudinal force) is represented on the vertical axis. The graph of FIG. 17C shows a characteristic curve formed using the values of the measurement data of the actually measured lateral force F_(y)(t) shown in FIG. 17B and the values of the time-series data of the transient response of the slip angle. In this case, symbol C of Formula (20) represents the above-mentioned lag time constant t₁ of the first-order-lag deformation response in the entire tire.

$\begin{matrix} \text{[Mathematical~~Formula~~6]} & \; \\ {\underset{({S^{\prime}{(t)}})}{\alpha^{\prime}(t)} = {\int_{0}^{t}{\left\lbrack {1 - {\exp \left( {- \frac{t - t^{\prime}}{C}} \right)}} \right\rbrack \underset{(\frac{{S{(t^{\prime})}}}{t})}{\frac{{\alpha \left( t^{\prime} \right)}}{t^{\prime}}}{t^{\prime}}}}} & (20) \end{matrix}$

Next, the characteristic curve is subjected to least-square regression to a smooth curve by using smooth curve functions, for example, spline functions. Then, regression calculation is performed so as to obtain a sum of square residuals between the least-square regression curve obtained through the least-square regression and the characteristic curve at that time (Step S260).

Next, it is judged whether or not the calculated sum of square residuals is smaller than the predetermined value and is minimum (Step S270). When the calculated sum of square residuals is not minimum, the set value of the lag time constant t₁ is corrected to thereby correct the first-order-lag response function (Step S280), and Steps S250 and S260 are repeated. The value of the lag time constant t₁ obtained when the sum of square residuals is minimum is determined as the value of the lag time constant t₁ for defining the first-order-lag response (Step S290).

Thus, the value of the lag time constant t₁ is determined so that the sum of square residuals becomes minimum for the following reason. As shown in FIG. 7C, in the transient state, the value of the lateral force varies depending on the cases where the slip angle is increased or decreased. This is because, with respect to the given slip angle (slip ratio), the actual slip angle (slip ratio) at the transient response time varies due to the first-order-lag deformation of the tread part, the belt part, and the side part according to the history in the past. Accordingly, the characteristic curve is formed by replacing the given slip angle (slip ratio) with the slip angle (slip ratio) at the transient response time, thereby obtaining a curve representing the same lateral force (longitudinal force) between the case where the slip angle is increased and the case where the slip angle is decreased, that is, a characteristic curve representing the lateral force (longitudinal force) or the like with respect to the slip angle in the steady state. As a result, when the characteristic curve in the transient state in which the value varies depending on the cases where the slip angle (slip ratio) is increased or decreased, the value of the set lag time constant t₁ is searched for while being corrected so that the sum of square residuals becomes minimum. The correction of the value of the lag time constant t₁ at that time can be performed by using a non-linear least-squares regression algorithm of the Newton-Raphson method. FIG. 17D shows an example of a smooth characteristic curve formed by using the determined value of the lag time constant. The characteristic curve corresponds to a characteristic curve of the lateral force in the steady state.

As described above, the lag time constant obtained when the sum of square residuals is minimum is searched for and determined.

Further, according to the present invention, in place of the calculation method for the tire transient response data shown in FIG. 13 in which the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) during cornering, or the time-series data of the longitudinal force F_(x)(t) during braking/driving is calculated, the following method can be used to calculate the time-series data of the lateral force F_(y)(t) and the torque M_(z)(t) during cornering, or the time-series data of the longitudinal force F_(x)(t) during braking/driving.

FIG. 18 is a flowchart showing a flow of the calculation method for the tire transient response data which is different from the method shown in FIG. 13. Specifically, FIG. 18 is the flowchart showing the flow of calculating the tire transient response data during cornering (baking/driving) when the slip angle (slip ratio) is given as the time-series data based on the tire dynamic model constituted by using a plurality of tire dynamic element parameters.

First, the time-series data of the slip angle α(t) (slip ratio S(t)) in which the slip angle changes at least within the range between 0 degrees and the predetermined angle is set (S310). Next, a value of the lateral force F_(y) or the torque M_(z) (longitudinal force F_(x)) in the steady state when the set slip angle α(t) (slip ratio S(t)) is given to the tire as the slip angle α (slip ratio S) in the steady state is acquired in advance (Step S320). The measurement data obtained through the actual measurement is stored in the memory 21 of the computing device through the data input section 12.

Then, the value of the lag time constant is loaded from the memory 21, and a response function of the first-order-lag response for specifying the deformation response of the tread part during cornering (braking/driving) is set. The value of the first-order-lag response loaded from the memory 21 contains the lag time constant t₁ of the response function for specifying the deformation response of the first-order lag in the entire tire. Computation of a convolution integral of the set response function with the time gradient of the time-series data of the set slip angle α(t) (slip ratio S(t)) is performed according to the above-mentioned Formula (20) where the lag time constant C is t₁, thereby calculating the time-series data of the transient response of the corrected slip angle α′(t) (corrected slip ratio S′(t)) in the tread part with respect to the road surface (Step S330).

Then, by calculating a value of the time-series data of the lateral force or self-aligning torque in the steady state corresponding to the value of the calculated time-series data of the corrected slip angle α′(t) (corrected slip ratio S′(t)) in the transient state, the lateral force or the torque (longitudinal force) in the transient state is calculated (Step S340).

This is because, it is assumed that, in the method of calculating the transient response, the value of the lateral force or the torque (longitudinal force) in the transient state is not based on the slip angle (slip ratio) actually given, but based on the corrected slip angle (corrected slip ratio) which is a correction result of the given slip angle (slip ratio) due to the first-order-lag deformation of the tread part. With this method, by using the data of the lateral force and the torque (longitudinal force) in the steady state and the corrected slip angle (corrected slip ratio), the time-series data of the torque (longitudinal force) in the transient state can be calculated simply and in a short period of time.

As described above, at least one of the linear parameter value and the non-linear parameter value containing the lag time constant in the tire dynamic model are calculated, and the value is related to each type of tire component member of the tire, that is, according to each type of tire component member, a table is created in advance so that at least one of the linear parameter value and the non-linear value containing the lag time constant are loaded. Thus, a tire designing method can be executed as described below.

Specifically, by using the calculation method for the tire transient response data, the tire transient response data (data of the lateral force, the torque, and the longitudinal force) is output. When the output data does not satisfy the set target condition, for example, when the output data does not match the target data within a range of an allowable error, the tire component member which defines the linear parameter value and the non-linear parameter value containing the lag time constant is changed for selection of other tire component member. Thus, at least one of the linear parameter value and the non-linear parameter value containing the lag time constant is changed according to the selected tire component member, thereby repeatedly calculating and outputting the tire transient response data. When the output data satisfies the target condition, the tire component member selected at that time is determined as the target tire component member. As a result, it is possible to design a desired tire for attaining the target condition.

Further, by using the calculation method for the tire transient response data, the tire transient response data is calculated and output, the tire transient response data is given to a vehicle model to which the tire is mounted, and a vehicle motion by the vehicle model is predicted, thereby making it possible to perform a simulation calculation of a motion behavior of the vehicle.

In the data processing method, the lag time constant of the first-order lag during cornering and the lag time constant of the first-order lag during braking/driving are separately determined, but the lag time constant of the first-order lag can be determined simultaneously in a state where values obtained at the time of cornering and values obtained at the time of braking/driving are mixed, and in addition, the lag time constant values of t_(r), t_(s), and t_(d) which are defined both in the cornering state and in the braking/driving state can be determined.

In the same manner as described above, the time-series data of the lateral force, torque, and longitudinal force obtained when the slip angle and the slip ratio are simultaneously given can be calculated at the same time.

In the data processing method, by using the measurement data in the tire transient state, the lag time constant value of the first-order lag during cornering or the lag time constant value of the first-order lag during braking/driving is determined. Alternatively, by enlarging the parameter whose value is to be determined, a part of the linear parameter value or the non-linear parameter value shown in FIGS. 3 and 10 may be determined with the above-mentioned lag time constant.

Next, a method and apparatus for evaluating a cornering characteristic of a tire according to the present invention will be described.

FIG. 19 a schematic structural diagram for illustrating a cornering characteristic measuring device 50 (hereinafter, referred to as “device 50”) which is an example of a device for evaluating a cornering characteristic of a tire according to the present invention. FIG. 19 illustrates an embodiment where, by using the apparatus 50, a tire 52 which is a target tire to be measured is rolled at a plurality of different rolling speeds, a tire dynamic element parameter value representing the cornering characteristic of the tire is derived, and further, a plot diagram representing a rolling speed dependency is displayed for each parameter value. The device 50 includes a cornering testing machine 54 and a measurement/evaluation unit 56. The measurement/evaluation unit 56 is connected with a display 58.

The cornering testing machine 54 is a known flat belt indoor testing machine which causes the tire 52 rotatably supported by the tire axis 62 to come in contact with the substitute road surface 64, which is a surface of the belt 60, to rotationally drive the belt 60, thereby causing the tire 52 to travel (roll) on the substitute road surface 64 of the belt 60. In the cornering testing machine 54 of this embodiment, a slip angle which changes step-wise in time-series is sequentially given to the tire 52 travelling on the substitute road surface 64, and a tire lateral force (lateral force) generated in the tire 52 in accordance with the slip angle is measured in time-series to obtain lateral force data. In the case where the slip angle (SA) of the tire has significantly changed due to a significant change in the steer angle or disturbance, the lateral force (SF) or self-aligning torque (SAT) with respect to the slip angle is generated with a time lag. In the specification, the tire characteristics at this time are referred to as “cornering characteristics”.

In this embodiment, the slip angle is input in a relatively small slip angle range in which the maximum value of the slip angle is 2.0 degrees or less. In other words, the tire lateral force generated in the tire 52 in accordance with the slip angle of the tire 52 as the measurement target in the vicinity of the steering neutral position at which the slip angle is relatively small, is measured. In the vicinity of the steering neutral position, the input slip angle and a response of the tire lateral force with respect to the slip angle have a substantially linear relationship. In this embodiment, the slip angle is input in the linear region having the substantially linear relationship.

The belt 60 is wound around a roller pair 68. The roller pair 68 is connected to a drive unit 66 including a motor (not shown). The substitute road surface 64 of the belt 60 moves through rotation of the roller pair 68 owing to the motor of the drive unit 66. The drive unit 66 is connected to the measurement unit 80 of the measurement/evaluation unit 56, which will be described later.

The tire axis 62 is provided to the axial tire support member 72. The axial tire support member 72 is rotationally driven about the Z-axis of FIG. 19 by the slip angle adjusting actuator 69 (hereinafter, referred to as “actuator”) as the slip angle adjusting means. The Z-axis of FIG. 19 is positioned on the equational plane of the tire 52, which is perpendicular to the rotation center axis of the tire 52 (that is, center of the tire axis 62). By rotationally driving the axial tire support member 72 about the Z-axis of FIG. 19, the slip angle of the rolling tire 52 (angle formed between the rolling direction of the tire 52, that is, the moving direction of the substitute road surface 64, and the equational plane of the tire 52) is varied. The actuator 69 is connected to the measurement unit 80 of the measurement/evaluation unit 56, which will be described later.

A sensor 74 capable of measuring the force applied to the tire axis 62 is provided to the axial tire support member 72. The sensor 74 measures the force applied to the tire axis 62 in the direction perpendicular to the tire equational plane (force in the Y-axis direction in FIG. 19), that is, the tire lateral force. It should be noted that the sensor 74 is not particularly limited as long as it is a device capable of measuring at least the tire lateral force applied to the tire axis 62, such as those using piezoelectric elements or those using strain gauges. The axial tire support member 72 is connected to a load applying device (not shown). When a predetermined load is applied by the load applying device during rolling of the tire 52, the tire 52 supported by the tire axis 62 is brought into contact with the substitute road surface 64 of the belt 60 by the predetermined contact load. The sensor 74 is connected to the measurement unit 80 of the measurement/evaluation unit 56, which will be described later.

The measurement/evaluation unit 56 is composed of the measurement unit 80 and the evaluation unit 90. FIG. 20 is a schematic structural diagram illustrating the measurement/evaluation unit 56. The measurement/evaluation unit 56 includes the measurement unit 80, the evaluation unit 90, a CPU 57, and a memory 59. The measurement/evaluation unit 56 is a computer in which respective sections of the measurement unit 80 and the evaluation unit 90 function when a program stored in the memory 59 is executed by the CPU 57.

It should be noted that a calculation and output program (hereinafter, referred to as “transient response calculation model program”) of a tire transient response calculation model which is a tire dynamic model of the invention is stored in the memory 59 in advance. The transient response calculation model is obtained by simplifying the tire dynamic model constituted by the plurality of tire dynamic element parameters by setting the condition of the slip angle within the linear region in which the maximum value thereof is 2.0 degrees or less, and simplifying the transient response of the tire lateral force. As described above, the tire dynamic model of this case is a model expressed by Formulae (1) to (8) shown in FIG. 3.

Formulae (1) to (8) representing the tire dynamic model are associated with the deformation (and delayed deformation) of individual tire members. By using Formulae (1) to (8), the cornering characteristics of the tire can be evaluated for cases where the characteristics of the respective components of the tire are changed individually. The above-mentioned tire dynamic model can be applied to (used in) the design of the tire. The tire dynamic model with the slip angle in the linear region, in which the maximum value thereof is 2.0 degrees or less, is simply expressed by Formulae (C) to (E) described bellow. The model expressed by those formulae is the transient response calculation model described above.

$\begin{matrix} \text{[Mathematical~~Formula~~7]} & \; \\ {{\alpha^{\prime}(t)} = {\int_{0}^{t}{\left\lbrack {1 - {\exp \left( {- \frac{t - t^{\prime}}{t_{3}}} \right)}} \right\rbrack \frac{{\alpha \left( t^{\prime} \right)}}{t^{\prime}}{t^{\prime}}}}} & (C) \\ {{F(t)} = {F_{ys}\left( {\alpha^{\prime}(t)} \right)}} & (D) \\ {{M(t)} = {M_{zs}\left( {\alpha^{\prime}(t)} \right)}} & (E) \end{matrix}$

In Formulae (C) to (E), F_(ys) (a), and M_(zs) (α) form a known steady slip angle dependence curve of the lateral force F_(y) and the self-aligning torque M_(z), which can be obtained in testing at an infinitesimal steering angular speed. Constant t₃ represents a time constant of the delayed response of the entire tire and is a value reflecting t_(s), t_(d), and t_(r) in the above-mentioned tire dynamic model. In the transient response calculation model as described above, the time constant t₃ becomes an important element in producing a difference between the steady response and the transient response.

There are two methods of calculating the time constant t₃.

As the first method when the lateral force is to be measured, as described above, a slip angle α(t) of the time-series is given to an actual tire, and data F_(y)(t) of the lateral force generated in the tire at this time is measured. After that, the following processing (a) and (b) is performed. The slip angle is set such that the slip angle increases from 0 and decreases after that.

(a) With respect to the measurement data group (α(t), F_(y)(t)) including the input slip angle α(t) and the lateral force data F_(y)(t) which is measurement data obtained at this time, conversion according to Formula (11) (conversion of α(t) into α′(t)) is performed using an adequate value as the time constant t₃, thereby obtaining the conversion data group (α′(t), F_(y)(t)). (b) The obtained conversion data group (α′(t), F_(y)(t)) is subjected to least square regression to a smooth curve function (with use of a spline function and the like), and the regression curve obtained at this time is calculated, whereby the sum of square residuals between the regression curve and the conversion data group (α′(t), F_(y)(t)) is calculated. By repeating the processing (a) and (b) as described above and using, for example, the non-linear least regression algorithm of a Newton-Raphson method, a value of t₃ is determined so that the above-mentioned sum of square residuals becomes minimum. The regression curve expressed by using the thus-determined value of t₃ with which the sum of square residuals becomes minimum (smooth curve function expressed by using the spline function and the like) corresponds to a slip angle dependence curve F_(ys)(α) of a steady lateral force.

The other method uses a linear tire model obtained by further simplifying the tire dynamic model by limiting the range of the slip angle to be input to the tire to the linear region of a low slip angle (absolute value of the slip angle α≦2.0°). In other words, F_(ys)(α) is represented as K_(y)·tan(α), and the time constant t₃ at which output data of the K_(y)·tan(α) matches the lateral force data F_(y)(t) in an allowable range is calculated.

In the linear region as described above, the output data F(t) corresponding to the lateral force is expressed by Formula (A) described bellow. In other words, time-series data of the transient response of the slip angle obtained by computing a convolution integral of the response function of a first-order-lag response specifying the deformation response of the tread part during cornering of the tire with a time gradient of the time-series data of the given slip angle is used.

$\begin{matrix} \text{[Mathematical~~Formula~~8]} & \; \\ {{F(t)} = {{K_{y} \cdot \tan}\left\{ {\int_{0}^{t}{\left\lbrack {1 - {\exp \left( {- \frac{t - t^{\prime}}{t_{3}}} \right)}} \right\rbrack \frac{{\alpha \left( t^{\prime} \right)}}{t^{\prime}}{t^{\prime}}}} \right\}}} & (A) \end{matrix}$

Here, K_(y) represents a cornering stiffness of the entire tire, which indicates a gradient at the rise of the lateral force when the slip angle is 0°. In the linear region, the relationship as in Formula (A) is established approximately. Further, assuming that the lateral force generated between the contact patch and the tire is simply transferred to the wheel side via the equivalent lateral stiffness K_(L), the time constant t₃ of the formula described above is approximately expressed by Formula (B) described bellow, the rolling speed of the tire being represented by V. In this case, K_(L) is the equivalent lateral stiffness set based on combined relations of the stiffnesses of the plurality of components of the tire. K_(L) and t₃ are important indexes that represent the transfer characteristics of the entire tire, and are indexes of the cornering characteristics of the tire. In this embodiment, the program of the output data by the linear tire model represented by the first-order lag system as described above, that is, program for calculating the output data F(t) according to Formulae (A) and (B) is stored in the memory 59 in advance.

$\begin{matrix} \text{[Mathematical~~Formula~~9]} & \; \\ {t_{3} = \frac{K_{y}}{K_{L}V}} & (B) \end{matrix}$

The measurement unit 80 includes a condition setting section 82, an operation controlling section 84, and a data acquiring section 86. The evaluation unit 90 includes a first parameter deriving section 92, a second parameter deriving section 94, and an evaluation section 96.

By controlling the operation of respective sections of the cornering testing machine 54, the measurement unit 80 inputs the slip angle that changes in time-series to the rolling tire 52 and acquires the tire lateral force data while causing the tire 52 to roll at a predetermined rolling speed and with a predetermined contact load.

The condition setting section 82 of the measurement unit 80 sets conditions of the slip angle that changes step-wise in time-series, rolling speed of the tire 52, and contact load of the tire, which are to be sequentially given to the tire 52 travelling on the substitute road surface 64.

The condition setting section 82 sets, at the time of acquiring an output signal of the tire lateral force, the conditions of the rolling speed or the contact load of the tire 52, and the slip angle which is to be input to the tire 52 and changes in time-series. In this embodiment, the condition setting section 82 sets the plurality of rolling speed conditions in advance. It should be noted that when a plot diagram for showing the load dependence is requested to be created in the evaluation section 96 to be described later with respect to the value of the tire dynamic element parameters representing the cornering characteristics, the condition setting section 82 only needs to set a plurality of magnitudes of the load to be applied to the tire, which is applied by the load applying device (not shown) described above.

Further, in the condition setting section 82, a time-series slip angle that changes step-wise as shown in FIG. 21A or 21B, for example, is set. By setting the slip angle that changes step-wise as described above, it is possible to have a relatively high frequency component contained in the time-series data of the slip angle to be input to the tire 52. In the present invention, the slip angle to be input preferably has a change rate of 0.1 to 0.5 (sec/degree) (0.25 (sec/degree) in the examples of FIGS. 21A and 21B). The reason for setting the slip angle within this range is because the change rate of the slip angle accompanying the actual steering of the vehicle at the time of high-speed travelling is in the range of about 0.1 to 0.5 (sec/degree). As described above, by setting the change rate of the slip angle to be the change rate of the slip angle accompanying the actual steering of the vehicle, measurement results of the cornering characteristics closer to the actual steering state of the vehicle can be obtained. Further, the maximum value of the absolute value of the slip angle according to the present invention is preferably 2.0 degrees or less. The reason for setting the maximum value of the slip angle in this range is because the range in which the lateral force data of the tire can be accurately expressed by the linear tire model expressed by the above-mentioned Formula (A) is within the range of the linear region having relatively small slip angle to be input to the tire. Further, by setting the slip angle to be input to the tire within the relatively small range, an effect of suppressing ablation of the tire of the measurement target due to the measurement can be obtained.

In the present invention, the upper limit value of the maximum value of the change rate of the slip angle to be input or the slip angle is set within a range corresponding to the actual travelling state of the vehicle. Accordingly, in the indoor cornering testing, the variation of the slip angle at the time of actual travelling of the vehicle can be reproduced, and the cornering characteristics of the vehicle at the time of the actual travelling of the vehicle can be reproduced with high accuracy. It should be noted that as for the slip angle to be input in time-series, the similar step-wise change in the slip angle is preferably repeated. By repeating the similar step-wise change and by repeatedly obtaining similar pieces of dynamic characteristics information, highly reliable and highly accurate information can be obtained.

The operation controlling section 84 controls the operation of each section of the cornering testing machine 54 based on the conditions of the rolling speed of the tire 52 and the time-series slip angle set in the condition setting section 82. The operation controlling section 84 is connected to the drive unit 66 and the actuator 69. The operation controlling section 84 controls the operation of the drive unit 66 (e.g., rotational speed of the motor) so that the tire 52 rolls at the rolling speed set in the condition setting section 82. Further, the operation controlling section 84 controls the operation of the actuator 69 so that the slip angle of the tire 52 changes under the condition of the time-series slip angle set in the condition setting section 82. Specifically, the set slip angle is sequentially input to the tire 52 in a state where the tire 52 is rolling at a single rolling speed set in the condition setting section 82. It should be noted that the time-series data of the slip angle to be input is also sequentially transmitted to the first parameter deriving section 92 of the evaluation unit 90.

The data acquiring section 86 obtains time-series output signals (lateral force data) of the tire lateral force corresponding to the slip angle when the slip angle is given to the rolling tire 52. The data acquiring section 86 is connected to the sensor 74 and acquires an output signal of the tire lateral force generated in the tire, which is output from the sensor 74, in time-series. The acquired time-series lateral force data of the tire lateral force is transmitted to the first parameter deriving section 92 of the evaluation unit 90.

The first parameter deriving section 92 of the evaluation unit 90 acquires time-series data of the slip angle transmitted from the operation controlling section 84 and time-series lateral force data acquired by the data acquiring section 86. Further, the first parameter deriving section 92 reads out the transient response calculation program (program of the linear tire model) from the memory 59 and derives a part of the tire dynamic element parameter representing the tire cornering characteristics using the linear tire model and the received data. Specifically, the first parameter deriving section 92 derives the value of the cornering stiffness K_(y) and the value of the lag time constant t₃ in Formula (A) by using the time-series data α(t) of the slip angle, so that the output data F(t) calculated by the program of the linear tire model is approximated to the lateral force data F_(y)(t) obtained through measurement. The value of the tire dynamic element parameter derived by the first parameter deriving section 92 is transmitted to the second parameter deriving section 94 and is stored in the memory 59. In the first parameter deriving section 92, the values of the cornering stiffness K_(y) and the time constant t₃ can be derived by, for example, least square regression. To be more specific, non-linear least regression algorithm of the Newton-Raphson method can be used, for example.

The second parameter deriving section 94 of the evaluation unit 90 derives a part of the values of the tire dynamic element parameters representing the tire cornering characteristics using the value of the tire dynamic element parameters received from the first parameter deriving section 92, information on the tire rolling speed, and the linear tire model described above. Specifically, the value of the equivalent lateral stiffness K_(L) of the tire is obtained by substituting the values of the cornering stiffness K_(y), the lag time constant t₃, and the tire rolling speed V in the above-mentioned Formula (B) specified by the linear tire model, and is stored in the memory 59.

When the value of the tire dynamic element parameters at a certain rolling speed is derived and stored in the memory 59, the device 50 causes the tire to roll at another rolling speed set in the condition setting section 82, and acquires the time-series tire lateral force data F_(y)(t) and slip angle α(t) at the changed rolling speed. With respect to the changed rolling speed, as described above, the values of the tire dynamic element parameters representing the tire cornering characteristics are respectively derived and stored in the memory 59. In the device 50, by repeating the procedure as described above under control of the CPU 57, the values of the tire dynamic element parameters representing the tire cornering characteristics under the conditions of the plurality of rolling speeds and loads, which have been set in the condition setting section 82, are derived and stored in the memory 59.

The evaluation unit 90 reads out the plurality of values of the tire dynamic element parameters stored as described above, and creates a plot diagram showing a correspondence between the rolling speed and the values of the respective tire dynamic element parameters at respective rolling speeds to output the diagram to the display 58, for example. The plot diagram shows the rolling speed dependency of the values of the respective dynamic element parameters. When a plurality of conditions of loads to be applied to the tire are set in the condition setting section 82, the evaluation unit 90 creates a plot diagram showing a correspondence between the loads and the values of the respective dynamic element parameters at the respective loads, and outputs the diagram to the display 58. The plot diagram shows the load dependency of the respective dynamic element parameters. As the tire rolling speed increases, the shape of the tire changes because of the expansion of the tread part in the radial direction due to the centrifugal force, which affects the cornering characteristics. By displaying the plot diagram representing the rolling speed dependency of the values of the respective dynamic element parameters, the evaluation section 96 provides detailed information on the tire cornering characteristics containing the change in the tire shape. In the actual evaluation of a vehicle, loads applied to the tires are not constant and change according to the operation of the steering wheel, brakes, and the like. Accordingly, evaluation of the load dependence is important.

FIG. 22 is a flowchart showing an example of a measurement method of tire cornering characteristics, which is carried out in the device 50. In the flowchart of FIG. 22, a case where the tire 52 is rolled at a plurality of different rolling speeds, values (t₃, K_(y), and K_(L)) of the tire dynamic element parameters representing the tire cornering characteristics at respective rolling speeds are derived, and a plot diagram representing the rolling speed dependency of the respective parameters is displayed is shown. First, the condition setting section 82 sets the conditions of the rolling speed of the tire 52, the load to be applied to the tire 52, and the time-series slip angle to be input to the tire 52 at the time of acquisition of the tire lateral force data (Step S402). As described above, for defining the slip angle to be given to the tire, the condition setting section 82 sets the slip angle that changes step-wise in time-series. In the present invention, as described above, the range of the change rate of the slip angle to be input is set to be within the range of 0.1 to 0.5 (sec/degree), and the maximum value of the slip angle to be input is set to 2.0 degrees or less. Thus, the condition of the slip angle is set so as to correspond to the variation of the slip angle accompanying the actual steering of the vehicle during high-speed travelling.

Next, the operation controlling section 84 controls the operation (e.g., rotational speed of a motor) of the drive unit 66 and causes the tire 52 to roll at one of the plurality of rolling speeds set in the condition setting section 82 (Step S404). While the tire 52 is rolling at the set rolling speed, the operation controlling section 84 controls the operation of the actuator 69 and inputs to the tire 52 the slip angle set in the condition setting section 82, which changes step-wise in time-series (Step S406). In a state where the tire 52 is rolling at the set rolling speed, the data acquiring section 86 acquires in time-series a signal of the lateral force data generated in the tire, which is output from the sensor 74 when the slip angle that changes in time-series is given to the tire 52 (Step S408).

Next, the first parameter deriving section 92 of the evaluation unit 90 derives the values of the part of the tire dynamic element parameters representing the tire cornering characteristics by using the time-series data of the slip angle transmitted from the operation controlling section 84, the tire lateral force data acquired by the data acquiring section 86, and the program of the linear tire model read out from the memory 59, and stores the values in the memory 59 (Step S410). Specifically, by subjecting the time-series data α(t) of the slip angle and the time-series tire lateral force data F_(y)(t) to the least square regression so as to be regressed to the above-mentioned Formula (A) (by making the output data F(t) in Formula (A) match the lateral force data F_(y)(t) in an allowable range), values of the cornering stiffness K_(y) and the time constant t₃ of Formula (A) are derived. The value of the tire dynamic element parameter derived by the first parameter deriving section 92 is transmitted to the second parameter deriving section 94 and is stored in the memory 59.

Next, the second parameter deriving section 94 of the evaluation unit 90 derives the values of the part of the tire dynamic element parameters representing the tire cornering characteristics by using the results obtained from the first parameter deriving section 92 and the information on the tire rolling speed, and stores the values in the memory 59 (Step S412). Specifically, the value of the equivalent lateral stiffness K_(L) of the tire is derived by substituting the values of the cornering stiffness K_(y), the time constant t₃, and the tire rolling speed V in the above-mentioned Formula (B), and is stored in the memory 59.

When the values of the cornering stiffness K_(y), the time constant t₃, and the equivalent lateral stiffness K_(L) of the tire dynamic element parameters are derived and stored with respect to a certain rolling speed (condition), judgment is made on whether the values of the tire dynamic element parameters have been calculated and stored with respect to all of the plurality of conditions of the rolling speeds that have been set (Step S414). When it is judged “No”, that is, when there is a rolling speed at which values of the tire dynamic element parameters are not yet calculated and stored among the plurality of set rolling speeds, the processing of Steps S404 to S414 is repeated after the rolling speed is changed (Step S418). The processing of Steps S404 to S414 as described above is repeated until it is judged “Yes” in Step S414, that is, until the values of the tire dynamic element parameters are derived for all of the plurality of set rolling speeds and are stored in the memory 59.

When it is judged “Yes” in Step S414, the evaluation section 96 reads out the plurality of stored values of the tire dynamic element parameters, creates, for example, a plot diagram showing a correspondence between the rolling speed and the values of the respective tire dynamic element parameters at respective rolling speeds, and outputs the diagram to the display 58 (Step S416). When a plurality of conditions of the load to be applied to the tire are set in the condition setting section 82, the evaluation section 96 can create a plot diagram showing the load dependency of the respective dynamic element parameters and showing a correspondence between the loads and the values of the respective dynamic element parameters at the respective loads, and output the diagram to the display 58. The measurement method of the cornering characteristics, which is an example of the evaluation method of the tire cornering characteristics of the present invention, is thus carried out.

Evaluation results of the tire cornering characteristics are shown below with respect to two tires A and B, whose evaluation results in the actual ride feeling test are different from each other, using the exemplary evaluation method of the tire cornering characteristics of the present invention.

The two tires A and B each have a size of 205/55R16, and cornering power CP and the stiffnesses (spring) in the lateral direction, longitudinal direction, and circumferential direction of the tire obtained as indoor characteristics and showing the characteristics in the steady state are substantially the same. The evaluation results of the actual ride feeling test show that the tire A has good steering stability and the tire B has poor steering stability.

In this embodiment, a plurality of conditions were set on a load to be applied to the tires, and respective tire dynamic element parameters obtained at different loads under the plurality of conditions were derived. Then, a plot diagram was created for showing a load dependency of each of the tire dynamic element parameters, that is, a correspondence between the load values and the tire dynamic element parameter values at different loads.

According to a first example, as regards a time-series slip angle to be applied to a tire, conditions were set such that the slip angle changes as shown in FIG. 21A. FIG. 23 is a graph showing a result of the first example performed under the above-mentioned conditions, in which time constants (the above-mentioned time constant t₃) of the tire A and the tire B at a specific rolling speed (120 km/h) and a specific load (4 kN) are respectively shown. Also, FIG. 24 is a graph showing a result of the first example performed under the above-mentioned conditions, in which values of the load dependencies of the lateral springs (the above-mentioned equivalent lateral stiffnesses K₁) of the tire A and the tire B are respectively shown. As can be determined based on FIGS. 23 and 24, the tire B has a time constant t₃ larger than that of the tire A, which means that the tire B is low in responsiveness as compared with the tire A. Also, the load dependency of the lateral spring of the tire B is weak in linearity, which indicates that the tire B is ill-balanced in which the cornering characteristic greatly changes along with the deformation of the tire due to the load. Further, the value of the lateral spring of the tire B remains low in most of the regions (across the different values set for the load), which means that the tire B is low in stiffness. Based on the above-mentioned information, it can be evaluated that the tire B has a poor cornering characteristic, that is, the tire B is inferior to the tire A in terms of steering stability. This evaluation result matches the evaluation result obtained in the in-vehicle feeling test. By using the cornering characteristic evaluation method of the present invention, it is possible to acquire an evaluation result of the cornering characteristic, which matches, with accuracy, the result acquired on the on-vehicle ride feeling test.

As a second example, conditions were set for a time-series slip angle to be applied to a tire such that the slip angle forms a sine curve of 1 Hz in frequency and ±1° in amplitude. FIG. 25 is a graph showing a result of the second example performed under the above-mentioned conditions, in which time constants (the above-mentioned time constant t₃) of the tire A and the tire B at a specific rolling speed (120 km/h) and a specific load (4 kN) are respectively shown. Also, FIG. 26 is a graph showing a result of the second example performed under the above-mentioned conditions, in which values of the load dependencies of the lateral springs (the above-mentioned equivalent lateral stiffnesses K_(L)) of the tire A and the tire B are respectively shown. As can be determined based on FIG. 25 and FIG. 26, even in the second example in which the slip angle to be applied to a tire forms a sine curve, the tire B has a time constant t₃ larger than that of the tire A, which means that the tire B is low in responsiveness as compared with the tire A. Further, the value of the cross spring of the tire B remains low in most of the regions (across the different values set for the load), which means that the tire B is low in stiffness. In the second example, it is also evaluated that the tire B has a low cornering characteristic, that is, the tire B is inferior to the tire A in terms of steering stability. This evaluation results matches the evaluation result obtained in the on-vehicle ride feeling test. However, according to the second example, it is difficult to determine that the tire B is ill-balanced in which a load dependency of the lateral spring is weak in linearity and thus the cornering characteristic greatly changes along with the deformation of the tire due to the load. On the other hand, according to the first example, in which the slip angle is set such that the slip angle changes stepwise in chronological order, it is possible to include a relatively high frequency component in time-series data of the slip angle to be applied to a tire 12, to thereby make it possible to obtain the load dependency of the lateral spring with higher accuracy. According to the tire cornering characteristic evaluation method of the present invention, it is preferable to set, as the slip angle to be applied to a tire, a slip angle which changes stepwise.

Next, another embodiment of the tire cornering characteristic evaluation method is described.

In the aforementioned embodiment, the cornering characteristic measuring device 50 is used to obtain the lateral force data F_(y)(t) on a tire which is actually manufactured as a test tire. According to this embodiment, however, in place of the actually-manufactured tire, the tire to be evaluated is approximated by a tire finite element model which the limited number of elements constitute so as to create a tire model, and simulation data generated through the rolling of the tire model, the data corresponding to a lateral force, is acquired as the lateral force data F_(y)(t).

FIG. 27 is a schematic structural diagram of an evaluation device 116 which reproduces a simulation in which a slip angle is applied to the tire finite element model which is in a rolling state, and evaluates the cornering characteristic of the tire based on the lateral force data acquired in the simulation.

The evaluation device 116 includes a data calculating unit 140 and the evaluation unit 150. The data calculating unit 140 includes a condition setting section 142, a characteristic value calculating section 144, a model creating section 146, and a simulation computing section 148. The evaluation unit 150 includes a first parameter deriving section 152, a second parameter deriving section 154, and an evaluation section 156. Those sections are each structured as a module performing a subroutine. In addition to those sections, the evaluation device 116 includes a CPU 117 for practically performing the processing of each of the above-mentioned sections, and a memory 119 for storing processing result acquired in each of the sections and a program of the above-mentioned linear tire model.

The first parameter deriving section 152, the second parameter deriving section 154, and the evaluation section 156 of the evaluation unit 150 each have a structure similar to the respective structures of the first parameter deriving section 92, the second parameter deriving section 94, and the evaluation section 96 of the measurement/evaluation unit 56 shown in FIG. 20, and a description thereof is omitted accordingly.

The condition setting section 142 of the data calculating unit 140 sets various conditions such as conditions for creating a tire finite element model, conditions for simulation computing, and conditions of a predicted performance, based on conditions input through a keyboard or a mouse (not shown). For example, values set as the conditions for creating a tire finite element model to be used in a tire behavior simulation include values of a shape parameter of each of the component members of a product tire and of a feature quantity parameter indicating a shape of each of the component members, a property value of each of the component members, and value of a feature quantity indicating the property value of each of the component members of the product tire.

The characteristic value calculating section 144 loads up tire product information stored in the memory 119 in advance. The tire product information includes a strain distribution, a stress distribution, and a strain energy distribution of a specific component member of the product tire. Based on the tire product information, the characteristic value calculating section 144 calculates a property value of a specific component member, such as a carcass cord, of the product tire. In calculating the property value, information on stress/strain curve which indicates a correspondence relation between a stress and a strain in a constituent material of the tire is stored in advance as a data base, which is used together with information on the strain distribution which is stored in the memory 119 in advance, to thereby calculate the characteristic value such as a viscoelasticity and a modulus of a component member of the product tire.

According to the characteristic value of the specific component member, which is calculated in the model creating section 146 and in the characteristic value calculating section 144, a part of the conditions for creating a tire model set by the condition setting section 142 in advance, such as a property value corresponding to the specific component member, is corrected as necessary, to thereby create a tire finite element model 160 shown in FIG. 28 based on the conditions for creating a tire model thus corrected. FIG. 28 shows a part of the tire finite element model 160. Through the creation of the model, position coordinates of node points of the tire finite element model 160, sets of numbers obtained by coding the node points constituting each finite element, the material constant number for each finite element, and the like, constitute at least a single file to be stored in the memory 119.

The simulation computing section 148 performs simulation computing on the tire finite element model 160 thus created, in accordance with conditions for the simulation computing, the conditions being set by the condition setting section 142. For example, a rim model (not shown), which is separately prepared, is attached to the tire finite element model 160, and the tire finite element model 160 is loaded with a constant force on an inner surface thereof so as to reproduce an inflation state, to thereby perform inflation processing. Further, the tire finite element model 160, which has been subjected to the inflation processing, is applied with a set load so as to be brought into contact with a rigid road surface model (not shown), to thereby create a tire finite element model 160 in a contact state. Further, the tire finite element model 160 in the contact state is applied with a translation speed and a rotation angular speed so as to reproduce a state in which the tire is rolling on the road surface, to thereby create a tire finite element model 160 in a rolling state.

In this state, the road surface is reproduced as a dry surface, and the simulation computing is performed based on this state. The simulation computing is not specifically limited, and a heretofore-known computing method can be employed therefor. For example, a slip angle may be applied to the tire to simulate a cornering behavior. In this case, lateral force data F_(y)(t) acting on a tire axial force is calculated as output data in the simulation. The simulation computing is performed based on conditions imitating the use conditions under which the tire is used (such as conditions of a load and a rolling speed).

The time-series lateral force data F_(y)(t) thus calculated is sent to the first parameter deriving section 152, together with the time-series slip angle α(t) which is applied in the simulation.

The first parameter deriving section 152 obtains, similarly to the first parameter deriving section 52, values for t₃ and K_(y) in the above-mentioned Formula (A) by using the slip angle α(t) such that the output data F(t) in Formula (A) matches the lateral force data F_(y)(t) within an allowable range. The second parameter deriving section 154 obtains, similarly to the second parameter deriving section 54, an equivalent lateral stiffness K_(L) by using the above-mentioned Formula (B) together with information on a rolling speed. The evaluation section 156 reads out a plurality of tire dynamic element parameters (t₃, K_(y), K_(L)) stored in the memory 119 so as to create a plot diagram for showing a speed dependency which indicates a correspondence relation between rolling speeds and respective dynamic element parameter values at different rolling speeds, and outputs the plot diagram to a display 118. Alternatively, the evaluation section 156 creates another plot diagram for showing a load dependency which indicates a correspondence between load values and respective dynamic element parameter values at different load values, and outputs the plot diagram to the display 118.

The specific component members of the tire finite element model 160 created by the model creating section 146 include, for example, a belt cover material and a carcass cord. The characteristic value calculating section 114 calculates property values of the belt cover material and the carcass cord in the tire to be evaluated, based on information on a strain distribution relating to the belt cover material and the carcass cord used in a product tire, the strain distribution being stored in the memory 119 in advance. In this case, the strain distribution of the carcass cord stored in the memory 119 in advance is obtained as follows. A carcass cord, which is used in a real product tire closely related to the tire to be evaluated, is in advance measured and stored, and the strain distribution of the carcass cord which is the measurement result of the closely related tire is read out and obtained as the strain distribution of the tire to be evaluated.

Specifically, first, a liner portion of the product tire is removed so as to reveal the carcass cord aligned on the product tire. At this time, a stress which has been applied in a tire manufacturing process still remains in the carcass cord. With the stress still remaining in the carcass cord, the carcass cord thus revealed is marked with identifiable indications (marking is performed on the carcass cord) at predetermined intervals (for example, at intervals of 5 to 30 mm). Then, those indications actually marked on the carcass cord is transferred, for example, to an inflexible tape. Intervals (L) at which the indications transferred on the inflexible tape are marked correspond to intervals at which indications are marked on the carcass cord in a state where the stress still remains in the carcass cord. Next, the marked carcass cord is taken out from the product tire without applying an extra stress, and intervals (L′) at which the indications marked in the above-mentioned marking on the carcass cord thus taken out are measured. The stress applied to the carcass cord in the above-mentioned manufacturing process is removed when the carcass cord is taken out. If the carcass cord is marked at the above-mentioned intervals (L′) before the application of stress in the manufacturing process, the stress applied in the manufacturing process turns the intervals (L′) into the intervals (L) at which the indications transferred to the inflexible tape are marked. With the technique described above, the intervals (L) and the intervals (L′) are obtained, and a strain ε of the carcass cord in the product tire can be obtained by a formula described below.

ε=(L−L′)/L′

The strain is obtained for each of a plurality of carcass cords and intervals at which indications are marked on a carcass cord are measured for each of the carcass cords, to thereby calculate the strain distribution in the product tire.

Based on information on the strain distribution of the carcass cord thus calculated, a property value is calculated for the carcass cord used in a tire to be evaluated. Specifically, based on the information on the strain distribution of the carcass cord described above, a property value (material constant such as Young's modulus and a Poisson's ratio) is calculated. For example, information on a stress/strain curve shown in FIG. 29, which indicates a correspondence relation between the stress applied to a carcass cord and the strain, is stored as a data base, and a property value of the carcass cord in the product tire is calculated based on the information on the strain. According to the stress/strain curve shown in FIG. 29, the tire finite element model has a reinforcing material portion, which corresponds to the carcass cord, set to have a material characteristic in which stiffness in a tensile direction and stiffness in a compression direction are different from each other. This is because, as understood from the embodiments described later, a modulus in the tensile direction and a modulus in the compression direction are made to be different from each other, thereby making it possible to acquire an evaluation result close to the actual evaluation result. A slope of the stress/strain curve of FIG. 29 at a predetermined portion (that is, a slope of a tangent line of the curve passing through a predetermined point) indicates a viscoelasticity of the carcass cord in a specific direction (a tensile direction or a compression direction). The property value of the carcass cord greatly varies depending on whether the compression stress is applied to the carcass cord, whether the tensile stress is applied to the carcass cord, and how much of strain is being caused in the carcass cord. By using the stress/strain curve described above, the property value of the carcass cord is obtained based on the above-mentioned strain distribution. Further, the above-mentioned stress distribution or an initial stress may be applied to a portion corresponding to the carcass cord of the tire finite element model, before performing the inflation process on the tire finite element model to be evaluated. An initial strain may also be applied.

The evaluation result of a tire based on the above-mentioned simulation is described according to a third example.

A real product tire (in a size 205/55R16 V550) was reproduced based on a finite element to create a tire finite element model 160. A carcass cord in the tire finite element model 160 was modeled based on a quadrangle membrane element defined by the anisotropy as shown in FIG. 29, and a rubber layer, a bead core, and the like were modeled based on a hexahedral or pentahedral solid element. A flat virtual road surface was defined by a rigid body having both a static friction coefficient and a dynamic friction coefficient of 1.3. The number of node points and the number of elements of the tire finite element model 160 were 118028 and 112294, respectively.

The simulation was performed in such a manner that a rim model was attached to the tire finite element model 160, and the tire finite element model 160 was subjected to inflation processing so as to be filled with an inner pressure of 200 kPa. After that, the tire finite element model 160 was applied with different loads (of 2, 4, 6 kN) so as to be brought into contact with a virtual road surface, and the road surface was displaced relatively so as to cause the tire finite element model 160 to roll at different rolling speeds (of 40, 80, 120, 160 km/h). When the simulation was performed under the different loads, the rolling speed was set to 40 km/h. When the simulation was performed under the different rolling speeds, the load was set to 4 kN. As the time-series slip angle α(t), a slip angle in a stepwise pattern of a trapezoidal shape as shown in FIG. 30 was used.

FIGS. 31A and 31B are plot diagrams for showing a speed dependency and a load dependency acquired in the simulation. The case A of FIGS. 31A and 31B shows results relating to the speed dependency and the load dependency, respectively, acquired through measurement of a real product tire, based on which the tire finite element model 160 is created, by using the cornering characteristic measuring device 50 shown in FIG. 19. The case B shows a case where a compression modulus and a tensile modulus are set to the same value not only for the modulus of the carcass code but also for the modulus of a portion corresponding to the belt cover material. The case C shows a case where the modulus of the carcass cord and the modulus of the belt cover material are set to be bilinear (the value of the compression modulus is set to be a hundredth of the value of the tensile modulus). The case D shows a case where the modulus of the carcass cord and the modulus of the belt cover material are set to be bilinear and an initial stress (initial tension) corresponding to a strain based on the strain distribution obtained by measuring the real product tire with the above-mentioned method is applied.

As can be understood from FIGS. 31A and 31B, the equivalent lateral stiffness K_(L) of the case C is close, as compared with the case B, to the data of the case A which is acquired from the lateral force data obtained through measurement of the real product tire. The equivalent lateral stiffness K_(L) of the case D substantially matches the data of the case A which is acquired from the lateral force data obtained through measurement of the real product tire. Accordingly, it is understood that, in the tire finite element model, the actual cornering characteristic can be evaluated with accuracy, by setting a material constant of the tire reinforcing material to be bilinear, or by applying an initial stress (initial tension) to the tire reinforcing material. In particular, it is understood that the data, which is obtained by setting a modulus of the tire reinforcing material to be bilinear as well as applying an initial stress (initial tension) to the tire reinforcing material, substantially matches the data of the case A which is acquired from the lateral force data obtained through measurement of the real product tire. As described above, the evaluation result of the cornering characteristic acquired by applying a slip angle to the product tire corresponds to the evaluation result of the cornering characteristic acquired in the on-vehicle ride feeling test. Therefore, the cornering characteristic, which is evaluated based on the result obtained through the simulation in which the finite element model of a tire is used, corresponds to the evaluation result of the cornering characteristic acquired in the on-vehicle ride feeling test.

Information on the speed dependency of the dynamic element parameter values (t₃, K_(y), K_(L)) obtained according to the present invention can be suitably used in, for example, the development of a tire improved in steering stability in high speed travelling.

Although the description of the present invention has been made in detail, the present invention is not limited to the above-mentioned embodiment. It is apparent that various modifications and changes are possible without departing from the scope of the gift of the present invention. 

1. A tire transient response data calculating method, for calculating tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, comprising the steps of: acquiring a value of at least one tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip angle provided to the tire dynamic model, the first-order-lag response specifying a deformation response of the tread part during cornering; and calculating, as transient response data during cornering, output data of at least one of a lateral force and self-aligning torque by using the tire dynamic model based on the calculated time-series data of the transient response of the slip angle.
 2. The tire transient response data calculating method according to claim 1, wherein the time-series data of the slip angle provided to the tire dynamic model is modified by torsional deformation of the tire dynamic model which is caused by a self-aligning torque during cornering, and the modified time-series data is used for calculating the time-series data of the transient response of the slip angle.
 3. The tire transient response data calculating method according to claim 2, wherein the torsional deformation of the tire which is generated by the self-aligning torque is represented by dividing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of previous time-series data of the self-aligning torque, by a value of a stiffness contained in the tire dynamic model, the first-order-lag response specifying a deformation response of a side part during cornering.
 4. The tire transient response data calculating method according to claim 1, wherein the output data calculated using the tire dynamic model comprises data of the lateral force corrected by lateral bending deformation of a belt part generated by the lateral force.
 5. The tire transient response data calculating method according to claim 4, wherein the lateral bending deformation of the belt part generated by the lateral force is represented by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of previous time-series data of the generated lateral force, the first-order-lag response specifying a deformation response of the belt part during cornering.
 6. A tire transient response data calculating method, for calculating tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model, comprising the steps of: previously acquiring values of at least one of a lateral force and a self-aligning torque in a steady state from actual measurement of a tire by providing a tire with the time-series data of the slip angle varying across at least a range between 0 degrees and a predetermined angle as the slip angle in the steady state; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip angle provided to the tire, the first-order-lag response specifying a deformation response of the tread part during cornering; and acquiring, as transient response data during cornering, the time-series data of at least one of the lateral force and self-aligning torque in a transient state by obtaining a value of at least one of the lateral force and self-aligning torque in the steady state corresponding to each value of the calculated time-series data of the transient response of the slip angle.
 7. A data processing method, in which a deformation response of a tread part which specifies a transient response during cornering in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of: previously acquiring measurement data of the transient response of at least one of a lateral force and self-aligning force during cornering of a tire by providing the tire with the time-series data of a slip angle as a measurement condition; setting a value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable, thereby making the tire dynamic model operable; performing simulating calculation including: obtaining the time-series data of a transient response of the slip angle between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the defined response function of the first-order-lag response with a time gradient of the time-series data of the slip angle provided to the tire as the measurement condition; calculating, as the time-series data of at least one of the lateral force and the self-aligning torque in a transient state during cornering, values of at least one of the lateral force and the self-aligning torque by using the tire dynamic model based on the obtained time-series data of the transient response of the slip angle; and obtaining a sum of square residuals between the calculated time-series data of at least one of the lateral force and self-aligning torque and the measurement data of the tire, repeating the simulating calculation while correcting the set value of the transient response parameter until the sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.
 8. A data processing method, in which a deformation response of a tread part which specifies a transient response during cornering in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of: previously acquiring measurement data of the transient response of at least one of a lateral force and a self-aligning torque during cornering of a tire by providing the tire with the time-series data of a slip angle, which varies across at least a range between 0 degrees and a predetermined angle while the slip angle reciprocates, as a measurement condition; setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; performing regression calculation including: obtaining the time-series data of a transient response of the slip angle between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the response function of the first-order-lag response with a time gradient of the time-series data of the slip angle provided to the tire as the measurement condition; subjecting a characteristic curve, which represents a values of at least one of the lateral force and the self-aligning torque with respect to values of the obtained time-series data of the transient response of the slip angle, to least square regression into a single smooth curve by using a curve function; and obtaining a sum of square residuals between the least square regression curve obtained by the least square regression and the characteristic curve; and repeating the regression calculation while correcting the set value of the transient response parameter until the calculated sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.
 9. A tire transient response data calculating method, for calculating tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, comprising the steps of: acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip ratio provided to the tire dynamic model, the first-order-lag response specifying a deformation response of the tread part during braking/driving,; and calculating, as transient response data during braking/driving, output data of a longitudinal force by using the tire dynamic model based on the time-series data of the transient response of the slip ratio.
 10. A tire transient response data calculating method, for calculating tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model, comprising the steps of: previously acquiring values of a longitudinal force in a steady state from actual measurement of the tire when the time-series data of the slip ratio varying across at least a range between 0 degrees and a predetermined slip ratio is provided as the slip ratio in the steady state; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model with a time gradient of the time-series data of the slip ratio, the first-order-lag response specifying a deformation response of the tread part during braking/driving; and acquiring, as transient response data during braking/driving, the time-series data of the longitudinal force in a transient state by obtaining a value of the longitudinal force in the steady state corresponding to each value of the calculated time-series data of the transient response of the slip ratio.
 11. A data processing method, in which a deformation response of a tread part which specifies a transient response during braking/driving of a tire in a tire dynamic model is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of: previously acquiring measurement data of the transient response of a longitudinal force during braking/driving of a tire by providing the tire with the time-series data of a slip ratio, which varies across at least a range between 0 degrees and a predetermined slip ratio while the slip ratio reciprocates, as a measurement condition; setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; performing regression calculation including: obtaining the time-series data of a transient response of the slip ratio between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the response function of the first-order-lag response with a time gradient of the time-series data of the slip ratio provided to the tire as the measurement condition; subjecting a characteristic curve, which represents values of the longitudinal force with respect to values of the obtained time-series data of the transient response of the slip ratio, to least square regression into a single smooth curve by using a curve function; and obtaining a sum of square residuals between the least square regression curve obtained by the least square regression and the characteristic curve; and repeating the regression calculation while correcting the set value of the transient response parameter until the calculated sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.
 12. A data processing method, in which a deformation response of a tread part which specifies a transient response during braking/driving in a tire dynamic model constituted by using at least one tire dynamic element parameter is set as a first-order-lag response to calculate a value of a transient response parameter that defines the first-order-lag response, comprising the steps of: previously acquiring measurement data of the transient response of a longitudinal force during braking/driving of a tire by providing the tire with the time-series data of a slip ratio in a longitudinal direction of the tire as a measurement condition; setting the value of the transient response parameter initially and defining a response function of the first-order-lag response, thereby making the tire dynamic model operable; performing simulating calculation including: obtaining the time-series data of a transient response of the slip ratio between the tread part and a road surface in the tire dynamic model by computing a convolution integral of the defined response function of the first-order-lag response with a time gradient of the time-series data of the slip ratio provided to the tire as the measurement condition; calculating a longitudinal force by using the tire dynamic model based on a value of the obtained time-series data of the transient response of the slip ratio, to obtain the time-series data of the longitudinal force in a transient state during braking/driving; and calculating a sum of square residuals of the calculated time-series data of the longitudinal force and the measurement data of the tire, repeating the simulating calculation while correcting the set value of the transient response parameter until the sum of square residuals becomes minimum, and determining the value of the transient response parameter obtained when the sum of square residuals becomes minimum as the value of the transient response parameter that defines the first-order-lag response.
 13. A tire designing method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, the tire transient response data calculating method including the steps of: acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during cornering, with a time gradient of the time-series data of the slip angle provided to the tire dynamic model; and calculating, as transient response data during cornering, output data of at least one of a lateral force and self-aligning torque by using the tire dynamic model based on the time-series data of the transient response of the slip angle; repeatedly calculating and outputting the tire transient response data while correcting the value of the tire dynamic element parameter or a value of a transient response parameter that defines the first-order-lag response by adjusting a tire component member that defines the tire dynamic element parameter or the first-order-lag response until the output transient response data satisfies a preset target condition; and determining the tire component member as a target tire component member when the output data satisfies the target condition.
 14. A tire designing method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model, the tire transient response data calculating method including the steps of: previously acquiring values of at least one of a lateral force and a self-aligning torque in a steady state from actual measurement of a tire by providing a tire with the time-series data of the slip angle varying across at least a range between 0 degrees and a predetermined angle as the slip angle in the steady state; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during cornering, with a time gradient of the time-series data of the slip angle provided to the tire; and calculating, as transient response data during cornering, the time-series data of at least one of the lateral force and self-aligning torque in a transient state by obtaining a value of one of the lateral force and self-aligning torque in the steady state corresponding to a value of the calculated time-series data of the transient response of the slip angle; repeatedly calculating and outputting the tire transient response data while correcting a value of a transient response parameter that defines the first-order-lag response by adjusting a tire component member that defines the first-order-lag response until the output transient response data satisfies a preset target condition; and determining the tire component member as a target tire component member when the output data satisfies the target condition.
 15. A tire designing method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model constituted by using at least one of tire dynamic element parameter, the tire transient response data calculating method including the steps of: acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during braking/driving, with a time gradient of the time-series data of the slip ratio provided to the tire dynamic model; and calculating, as transient response data during braking/driving, output data of a longitudinal force by using the tire dynamic model based on the time-series data of the transient response of the slip ratio; repeatedly calculating and outputting the tire transient response data while correcting a value of the tire dynamic element parameter or a value of a transient response parameter that defines the first-order-lag response by adjusting a tire component member that defines one of the tire dynamic element parameter or the first-order-lag response until the output transient response data satisfies a preset target condition; and determining the tire component member as a target tire component member when the output data satisfies the target condition.
 16. A tire designing method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model, the tire transient response data calculating method including the steps of: previously acquiring a value of a longitudinal force in a steady state from actual measurement of the tire when the time-series data of the slip ratio varying across at least a range between 0 degrees and a predetermined slip ratio is provided as the slip ratio in the steady state; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during braking/driving, with a time gradient of the time-series data of the slip ratio; and acquiring, as transient response data during braking/driving, the time-series data of the longitudinal force in a transient state by obtaining a value of the longitudinal force in the steady state corresponding to a value of the calculated time-series data of the transient response of the slip ratio; repeatedly calculating and outputting the tire transient response data while correcting a value of a transient response parameter that defines the first-order-lag response by adjusting a tire component member that defines the first-order-lag response until the output transient response data satisfies a preset target condition; and determining the tire component member as a target tire component member when the output data satisfies the target condition.
 17. A vehicle motion predicting method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, the tire transient response data calculating method including the steps of: acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during cornering, with a time gradient of the time-series data of the slip angle provided to the tire dynamic model; and calculating, as transient response data during cornering, output data of at least one of a lateral force and self-aligning torque by using the tire dynamic model based on the time-series data of the transient response of the slip angle; and predicting a vehicle motion based on a vehicle model by providing the transient response data to an axle portion of the vehicle model.
 18. A vehicle motion predicting method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during cornering with a slip angle provided as time-series data based on a tire dynamic model, the tire transient response data calculating method including the steps of: previously acquiring values of at least one of a lateral force and a self-aligning torque in a steady state from actual measurement of a tire by providing a tire with the time-series data of the slip angle varying across at least a range between 0 degrees and a predetermined angle as the slip angle in the steady state; calculating the time-series data of a transient response of the slip angle between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during cornering, with a time gradient of the time-series data of the slip angle provided to the tire; and acquiring, as transient response data during cornering, the time-series data of one of the lateral force and self-aligning torque in a transient state by obtaining a value of at least one of the lateral force and self-aligning torque in the steady state corresponding to a value of the calculated time-series data of the transient response of the slip angle; and predicting a vehicle motion based on a vehicle model by providing the transient response data to an axle portion of the vehicle model.
 19. A vehicle motion predicting method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model constituted by using at least one tire dynamic element parameter, the tire transient response data calculating method including the steps of: acquiring a value of the tire dynamic element parameter constituting the tire dynamic model, thereby making the tire dynamic model operable; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during braking/driving, with a time gradient of the time-series data of the slip ratio provided to the tire dynamic model; and calculating, as transient response data during braking/driving, output data of a longitudinal force by using the tire dynamic model based on the time-series data of the transient response of the slip ratio; and predicting a vehicle motion based on a vehicle model by providing the transient response data to an axle portion of the vehicle model.
 20. A vehicle motion predicting method, comprising the steps of: calculating and outputting tire transient response data by using a tire transient response data calculating method for calculating the tire transient response data during braking/driving with a slip ratio in a longitudinal direction of a tire provided as time-series data based on a tire dynamic model, the tire transient response data calculating method including the steps of: previously acquiring values of a longitudinal force in a steady state from actual measurement of the tire when the time-series data of the slip ratio varying across at least a range between 0 degrees and a predetermined slip ratio is provided as the slip ratio in the steady state; calculating the time-series data of a transient response of the slip ratio between a tread part and a road surface in the tire dynamic model by computing a convolution integral of a response function of a first-order-lag response of the tire dynamic model, which specifies a deformation response of the tread part during braking/driving, with a time gradient of the time-series data of the slip ratio; and acquiring, as transient response data during braking/driving, the time-series data of the longitudinal force in a transient state by obtaining a value of the longitudinal force in the steady state corresponding to a value of the calculated time-series data of the transient response of the slip ratio; and predicting a vehicle motion based on a vehicle model by providing the transient response data to an axle portion of the vehicle model.
 21. A method of evaluating a cornering characteristic of a tire when a slip angle is provided as time-series data, comprising the steps of: acquiring time-series lateral force data with respect to the time-series data of the slip angle, regarding the tire which generates a tire lateral force by being brought into contact with a ground in a contact patch and rolling at a predetermined rolling speed; and deriving a value of a tire dynamic element parameter representing the cornering characteristic of the tire by using: a transient response calculation model that is constituted by using at least one tire dynamic element parameter and is used to calculate output data corresponding to the lateral force data of a transient response generated in the tire with respect to the time-series data of the slip angle; and the acquired lateral force data, wherein the step of deriving the value of the tire dynamic element parameter is performed by using the time-series data of a transient response of the slip angle obtained by computing a convolution integral of a response function of a first-order-lag response of the transient response calculation model, which specifies a deformation response of a tread part of the tire during cornering, with a time gradient of the time-series data of the slip angle provided to the transient response calculation model.
 22. The method of evaluating a cornering characteristic of a tire according to claim 21, wherein the step of acquiring the lateral force data is performed by reproducing an evaluation target tire with a tire finite element model, which is obtained by dividing the evaluation target tire into a finite number of elements, and by using a finite element method to acquire, as the lateral force data, simulation data of the lateral force acting on the tire finite element model which is brought into contact with the ground in the contact patch and caused to roll at the predetermined rolling speed and to which a time-series slip angle is input.
 23. The method of evaluating a cornering characteristic of a tire according to claim 22, wherein the tire finite element model is coupled with a rim model for reproducing a rim, and reproduces the tire brought into contact with the ground in the contact patch and rolling at the predetermined rolling speed by bringing the tire finite element model into contact with a flat virtual road surface in the contact patch and moving the tire finite element model at the predetermined rolling speed relatively to the virtual road surface.
 24. The method of evaluating a cornering characteristic of a tire according to claim 22, wherein the tire finite element model includes a reinforcement material portion corresponding to a cord reinforcing material of the tire, the reinforcement material portion having such a material characteristic that a stiffness along a tensile direction and a stiffness along a compression direction are different from each other.
 25. The method of evaluating a cornering characteristic of a tire according to claim 22, wherein the tire finite element model is subjected to an inflation process for simulating tire inflation, and the inflation process is performed after one of an initial stress and an initial strain is applied to at least one portion of the tire finite element model.
 26. The method of evaluating a cornering characteristic of a tire according to claim 21, wherein the step of acquiring the lateral force data is performed by providing a time-series slip angle to the tire while bringing the tire into contact with the ground in the contact patch and rolling the tire at the predetermined rolling speed, and by acquiring, as the lateral force data, measurement data of the time-series tire lateral force corresponding to the slip angle.
 27. The method of evaluating a cornering characteristic of a tire according to claim 21, wherein: the transient response calculation model is represented by setting a transient response of the tire lateral force with respect to the slip angle as a first-order-lag response; and the slip angle to be input ranges within such a linear range that the slip angle and the response of the tire lateral force with respect to the slip angle are in a substantially linear relation.
 28. The method of evaluating a cornering characteristic of a tire according to claim 21, wherein the step of deriving the value of the tire dynamic element parameter is performed by using the time-series data of the input slip angle and the time-series lateral force data corresponding to the time-series data of the slip angle in such a manner that the output data of the transient response calculation model matches the time-series lateral force data within an allowable range.
 29. The method of evaluating a cornering characteristic of a tire according to claim 21, wherein the slip angle ranges from −2.0 degrees to 2.0 degrees.
 30. The method of evaluating a cornering characteristic of a tire according to claim 29, wherein: when the output data is represented by F(t), the transient response calculation model contains a formula represented by Formula (A) described bellow; and the step of deriving the value of the tire dynamic element parameter includes obtaining a value of a cornering stiffness K_(y) and a value of a time constant t₃, which are dynamic element parameters of Formula (A) described bellow, by using the input time-series slip angle α(t) in such a manner that the F(t) within Formula (A) described bellow matches the time-series lateral force data F_(y)(t) corresponding to the slip angle α(t) within the allowable range. $\begin{matrix} \text{[Mathematical~~Formula~~1]} & \; \\ {{F(t)} = {{K_{y} \cdot \tan}\left\{ {\int_{0}^{t}{\left\lbrack {1 - {\exp \left( {- \frac{t - t^{\prime}}{t_{3}}} \right)}} \right\rbrack \frac{{\alpha \left( t^{\prime} \right)}}{t^{\prime}}{t^{\prime}}}} \right\}}} & (A) \end{matrix}$
 31. The method of evaluating a cornering characteristic of a tire according to claim 30, wherein: the output data calculated by the transient response calculation model comprises data of the tire lateral force transmitting to a wheel side via an equivalent stiffness K_(L) of an entirety of the tire with respect to an input of the slip angle; and when the predetermined rolling speed at a time of acquiring the lateral force data is assumed to be V, the step of deriving the value of the tire dynamic element parameter includes deriving a value of the equivalent stiffness K_(L) representing a transmission characteristic of the tire lateral force by substituting the value of the cornering stiffness K_(y) and the value of the time constant t₃, which are obtained by using the above-mentioned Formula (A), and the rolling speed V, into Formula (B) described bellow. $\begin{matrix} \text{[Mathematical~~Formula~~2]} & \; \\ {t_{3} = \frac{K_{y}}{K_{L}V}} & (B) \end{matrix}$
 32. An apparatus for evaluating a cornering characteristic of a tire under a condition in which a slip angle is provided as time-series data, comprising: a data acquiring section for acquiring time-series lateral force data with respect to a time-series slip angle, regarding the tire being brought into contact with a ground in a contact patch and rolling at a predetermined rolling speed; and a deriving section for deriving a value of a tire dynamic element parameter representing the cornering characteristic of the tire by using: a transient response calculation model that is constituted by using at least one tire dynamic element parameter and is used to calculate output data corresponding to the lateral force data of a transient response generated in the tire with respect to the slip angle; and the lateral force data, wherein the deriving section derives the value of the tire dynamic element parameter by using the time-series data of a transient response of the slip angle obtained by computing a convolution integral of a response function of a first-order-lag response, which specifies a deformation response of a tread part of the tire during cornering, with a time gradient of the time-series data of the slip angle provided to the transient response calculation model. 